Claude-3 Sonnet on 3.MD.D.8-triangle
Common Core Standard 3.MD.D.8-triangle
This standard covers the following:
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Problem: An equilateral triangle has a perimeter of 990cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 990 cm. Step 1: Set up the equation using the given information. 990 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 990 / 3 side length = 330 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 990 cm is 330 cm. ### Answer: 330 cm
Expected answer: 330
Correct? Yes
Problem: A triangle has a perimeter of 997m. Two of its sides have lengths of 2m and 667m. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 997 meters. - Two sides of the triangle have lengths of 2 meters and 667 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Side 1 + Side 2 + Side 3 997 = 2 + 667 + x Rearranging the terms, we get: x = 997 - 2 - 667 x = 328 Therefore, the length of the third side of the triangle is 328 meters. ### Answer: 328
Expected answer: 328
Correct? Yes
Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is given by: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 579 cm. Step 1: Set up the equation using the given information. 579 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 579 / 3 Side length = 193 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 579 cm is 193 cm. ### Answer: 193 cm
Expected answer: 193
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 684 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 684 meters = 3 × Side length Side length = 684 meters / 3 Side length = 228 meters Therefore, each side of the equilateral triangle has a length of 228 meters. ### Answer: 228
Expected answer: 228
Correct? Yes
Problem: A triangle has a perimeter of 503 meters. One side of the triangle is 223 meters long and another side is 46 meters long. What is the length of the remaining side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 503 meters. - One side of the triangle is 223 meters long. - Another side of the triangle is 46 meters long. Let's represent the length of the remaining side as x. According to the perimeter formula: Perimeter = Sum of the lengths of all three sides 503 = 223 + 46 + x Rearranging the equation to find x: x = 503 - 223 - 46 x = 234 meters Therefore, the length of the remaining side of the triangle is 234 meters. ### Answer: 234
Expected answer: 234
Correct? Yes
Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 105 meters. Step 1: Set up the equation using the given information. 105 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 105 / 3 side length = 35 meters Therefore, the length of each side of the equilateral triangle with a perimeter of 105 meters is 35 meters. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: An equilateral triangle has a perimeter of 306cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 306 cm. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 306 cm = 3 × Side length Side length = 306 cm / 3 Side length = 102 cm Therefore, each side of the equilateral triangle has a length of 102 cm. ### Answer: 102
Expected answer: 102
Correct? Yes
Problem: An equilateral triangle has a perimeter of 33 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 33 cm. Step 1: Set up the equation using the given information. 33 cm = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 33 cm / 3 side length = 11 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 33 cm is 11 cm. ### Answer: 11 cm
Expected answer: 11
Correct? Yes
Problem: A triangle has a perimeter of 861m. Two of the sides are known to be 192m and 159m in length. Can you find the length of the third side?
Claude-3 Sonnet:
To find the length of the third side of a triangle, we can use the property that the sum of the lengths of all three sides is equal to the perimeter of the triangle. Given information: - Perimeter of the triangle = 861 meters - Length of one side = 192 meters - Length of another side = 159 meters Let the length of the third side be x. According to the property of the perimeter of a triangle, we have: 192 + 159 + x = 861 Rearranging the terms, we get: x = 861 - 192 - 159 x = 510 meters Therefore, the length of the third side of the triangle is 510 meters. ### Answer: 510
Expected answer: 510
Correct? Yes
Problem: A triangle has a perimeter of 489 centimeters. If each of its sides is of equal length, what is the length of one side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the triangle given that the perimeter (the sum of all sides) is 489 centimeters and all sides are equal. Given information: - The perimeter of the triangle is 489 centimeters. - The triangle has three equal sides. Let's represent the length of one side as x. Since the triangle has three equal sides, we can write the following equation: x + x + x = 489 Simplifying the equation: 3x = 489 Dividing both sides by 3: x = 489 / 3 x = 163 Therefore, the length of one side of the triangle is 163 centimeters. ### Answer: 163
Expected answer: 163
Correct? Yes
Problem: An equilateral triangle has a perimeter of 696 meters. What is the length of each side of this triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 696 meters. Step 1: Set up the equation using the given information. 696 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 696 / 3 side length = 232 meters Therefore, the length of each side of the equilateral triangle with a perimeter of 696 meters is 232 meters. ### Answer: 232
Expected answer: 232
Correct? Yes
Problem: The perimeter of a triangle is 804m. One side of the triangle is 180m long, and another side is 579m long. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 804 meters. - One side of the triangle is 180 meters long. - Another side of the triangle is 579 meters long. Let's represent the length of the third side as x. The perimeter of a triangle is the sum of the lengths of all three sides. Perimeter = Side 1 + Side 2 + Side 3 804 = 180 + 579 + x Rearranging the equation to find x: x = 804 - 180 - 579 x = 45 meters Therefore, the length of the third side of the triangle is 45 meters. ### Answer: 45
Expected answer: 45
Correct? Yes
Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 915 cm. Step 1: Set up the equation using the given information. 915 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 915 / 3 side length = 305 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 915 cm is 305 cm. ### Answer: 305
Expected answer: 305
Correct? Yes
Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 564 cm. Step 1: Set up the equation using the given information. 564 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 564 / 3 Side length = 188 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 564 cm is 188 cm. ### Answer: 188
Expected answer: 188
Correct? Yes
Problem: An equilateral triangle has a perimeter of 594 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 594 cm. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 594 cm = 3 × Side length Side length = 594 cm / 3 Side length = 198 cm Therefore, each side of the equilateral triangle has a length of 198 cm. ### Answer: 198
Expected answer: 198
Correct? Yes
Problem: An equilateral triangle has a perimeter of 453 cm. How long is each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the given information about the perimeter of the equilateral triangle and the fact that all sides of an equilateral triangle are equal in length. Given information: - The perimeter of the equilateral triangle is 453 cm. - In an equilateral triangle, all three sides have equal lengths. Let's represent the length of each side as x. Since the perimeter is the sum of all the sides, we can write the equation: Perimeter = Side 1 + Side 2 + Side 3 453 = x + x + x 453 = 3x Dividing both sides by 3, we get: x = 453 / 3 x = 151 Therefore, each side of the equilateral triangle has a length of 151 cm. ### Answer: 151
Expected answer: 151
Correct? Yes
Problem: A triangle has a total perimeter of 898m. The lengths of two of its sides are 250m and 435m respectively. Can you find the length of the third side of the triangle?
Claude-3 Sonnet:
To find the length of the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given information: - Total perimeter of the triangle = 898 meters - Length of one side = 250 meters - Length of another side = 435 meters Step 1: Find the sum of the lengths of the two known sides. Sum of the lengths of the two known sides = 250 meters + 435 meters = 685 meters Step 2: Find the length of the third side using the triangle inequality theorem. Length of the third side = Total perimeter - Sum of the lengths of the two known sides Length of the third side = 898 meters - 685 meters = 213 meters Therefore, the length of the third side of the triangle is 213 meters. ### Answer: 213
Expected answer: 213
Correct? Yes
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to use the given information and the properties of an equilateral triangle. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The total perimeter of the triangle is 405 cm. Properties of an equilateral triangle: - All three angles are equal to 60 degrees. - All three sides have equal lengths. Step 1: Find the length of one side of the equilateral triangle. Let the length of one side be x. Since all sides are equal, the total perimeter is three times the length of one side. Total perimeter = 3 × x 405 cm = 3x x = 405 cm / 3 x = 135 cm Therefore, the length of each side of the equilateral triangle is 135 cm. ### Answer: 135 cm
Expected answer: 135
Correct? Yes
Problem: Somehow you got lost in the forest and got trapped in a mysterious place where you find an equilateral triangle-shaped space. The total perimeter of this space is 612 meters. Can you find out the length of each side of this triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the properties of an equilateral triangle and the formula for the perimeter of a triangle. Given information: - The space is an equilateral triangle. - The total perimeter of the space is 612 meters. Properties of an equilateral triangle: - All three sides have equal lengths. - All three angles are equal to 60 degrees. The perimeter of a triangle is the sum of the lengths of its three sides. Let's denote the length of each side as x. Since the triangle is equilateral, all three sides have the same length x. Perimeter of the triangle = Sum of the lengths of the three sides 612 meters = x + x + x 612 meters = 3x Dividing both sides by 3, we get: x = 612 meters / 3 x = 204 meters Therefore, the length of each side of the equilateral triangle-shaped space is 204 meters. ### Answer: 204
Expected answer: 204
Correct? Yes
Problem: An equilateral triangle has a perimeter of 591 cm. Can you find the length of each side of this triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the given information about the perimeter of the equilateral triangle and the fact that all sides of an equilateral triangle are equal in length. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 591 cm. Step 1: Find the length of one side of the triangle. Perimeter of a triangle = Sum of the lengths of all three sides Let the length of each side be x. Perimeter = x + x + x 591 cm = 3x x = 591 cm / 3 x = 197 cm Step 2: Check the answer by substituting the value of x into the perimeter formula. Perimeter = x + x + x Perimeter = 197 cm + 197 cm + 197 cm Perimeter = 591 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 591 cm is 197 cm. ### Answer: 197 cm
Expected answer: 197
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 858 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 858 meters = 3 × Side length Side length = 858 meters / 3 Side length = 286 meters Therefore, each side of the equilateral triangle has a length of 286 meters. ### Answer: 286
Expected answer: 286
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543 meters. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 543 meters. Step 1: Set up the equation using the given information. 543 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 543 / 3 Side length = 181 Therefore, the length of each side of the equilateral triangle with a perimeter of 543 meters is 181 meters. ### Answer: 181
Expected answer: 181
Correct? Yes
Problem: A triangle has three equal sides. If the perimeter of the triangle is 255 meters, what is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the triangle given that it is an equilateral triangle (all sides are equal) and the perimeter is 255 meters. Given information: - The triangle is equilateral (all sides are equal). - The perimeter of the triangle is 255 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = 3 × side length Step 2: Substitute the given perimeter value and solve for the side length. 255 meters = 3 × side length Side length = 255 meters / 3 Side length = 85 meters Therefore, the length of each side of the equilateral triangle is 85 meters. ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: An equilateral triangle has a perimeter of 570mm. Find the length of each side of this triangle.
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is given by: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 570 mm. Step 1: Set up the equation using the given information. 570 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 570 / 3 side length = 190 mm Therefore, the length of each side of the equilateral triangle with a perimeter of 570 mm is 190 mm. ### Answer: 190 mm
Expected answer: 190
Correct? Yes
Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 129 meters. Step 1: Set up the equation using the given information. 129 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 129 / 3 side length = 43 meters Therefore, the length of each side of the equilateral triangle with a perimeter of 129 meters is 43 meters. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858 meters. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 858 meters. Step 1: Set up the equation using the given information. 858 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 858 / 3 side length = 286 Therefore, the length of each side of the equilateral triangle is 286 meters. ### Answer: 286
Expected answer: 286
Correct? Yes
Problem: A triangle has a perimeter of 513 km, and it's known to be an equilateral triangle - meaning all three sides are of equal length. Can you determine how long each side of this triangle is?
Claude-3 Sonnet:
To solve this problem, we need to use the given information and the properties of an equilateral triangle. Given information: - The perimeter of the triangle is 513 km. - The triangle is an equilateral triangle, which means all three sides have equal lengths. In an equilateral triangle, the sum of the lengths of all three sides is equal to the perimeter. Let's represent the length of each side as x. Since there are three sides of equal length, we can write: x + x + x = 513 Simplifying the equation: 3x = 513 Dividing both sides by 3: x = 513 / 3 x = 171 Therefore, the length of each side of the equilateral triangle is 171 km. ### Answer: 171
Expected answer: 171
Correct? Yes
Problem: A triangular field has a perimeter of 828 meters. Two sides of the field are 105 and 434 meters long. How long is the third side of the field?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangular field is 828 meters. - Two sides of the field are 105 meters and 434 meters long. Let's represent the length of the third side as x. According to the perimeter formula for a triangle: Perimeter = Side 1 + Side 2 + Side 3 828 = 105 + 434 + x Rearranging the terms, we get: x = 828 - 105 - 434 x = 289 meters Therefore, the length of the third side of the triangular field is 289 meters. ### Answer: 289
Expected answer: 289
Correct? Yes
Problem: The perimeter of a triangle is 773 cm. Two of its sides measure 37 cm and 559 cm, respectively. Find the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 773 cm. - Two sides of the triangle measure 37 cm and 559 cm. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 773 cm = 37 cm + 559 cm + x Rearranging the terms, we get: x = 773 cm - 37 cm - 559 cm x = 177 cm Therefore, the length of the third side of the triangle is 177 cm. ### Answer: 177
Expected answer: 177
Correct? Yes
Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 714 meters. Step 1: Set up the equation using the given information. 714 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 714 / 3 side length = 238 meters Therefore, the length of each side of the equilateral triangle with a perimeter of 714 meters is 238 meters. ### Answer: 238
Expected answer: 238
Correct? Yes
Problem: In a large triangular garden, one of its sides is 147m and another side is 590m. If the perimeter of the garden is 792m, can you find the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - One side of the triangle is 147 meters. - Another side of the triangle is 590 meters. - The perimeter of the triangle is 792 meters. Let's represent the length of the third side as x. The perimeter of a triangle is the sum of the lengths of all three sides. Perimeter = Side 1 + Side 2 + Side 3 792 = 147 + 590 + x Rearranging the terms, we get: x = 792 - 147 - 590 x = 55 meters Therefore, the length of the third side of the triangular garden is 55 meters. ### Answer: 55
Expected answer: 55
Correct? Yes
Problem: The perimeter of a triangle is 871 meters. One of the sides is 321 meters long and another is 528 meters long. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 871 meters. - One side of the triangle is 321 meters long. - Another side of the triangle is 528 meters long. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Side 1 + Side 2 + Side 3 871 = 321 + 528 + x Rearranging the terms, we get: x = 871 - 321 - 528 x = 22 meters Therefore, the length of the third side of the triangle is 22 meters. ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: A triangle has a perimeter of 991m. Two sides of the triangle measure 424m and 246m respectively. Find the length of the third side of the triangle.
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 991 meters. - The length of one side is 424 meters. - The length of another side is 246 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 991 = 424 + 246 + x Rearranging the terms, we get: x = 991 - 424 - 246 x = 321 Therefore, the length of the third side of the triangle is 321 meters. ### Answer: 321
Expected answer: 321
Correct? Yes
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 936 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 936 meters = 3 × Side length Side length = 936 meters / 3 Side length = 312 meters Therefore, each side of the equilateral triangle with a perimeter of 936 meters is 312 meters long. ### Answer: 312
Expected answer: 312
Correct? Yes
Problem: A triangle has a perimeter of 721m. Two of its sides have lengths of 204m and 195m, respectively. What is the length of the third side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 721 meters. - The length of one side is 204 meters. - The length of another side is 195 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 721 = 204 + 195 + x Rearranging the equation: x = 721 - 204 - 195 x = 322 Therefore, the length of the third side of the triangle is 322 meters. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 201 meters. Step 1: Set up the equation using the given information. 201 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 201 / 3 side length = 67 Therefore, the length of each side of the equilateral triangle with a perimeter of 201 meters is 67 meters. ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is given by: Perimeter = 3 × side length Given information: - The perimeter of the large equilateral triangle is 756 meters. Step 1: Set up the equation using the given information. 756 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 756 / 3 side length = 252 meters Therefore, the length of each side of the large equilateral triangle is 252 meters. ### Answer: 252 meters
Expected answer: 252
Correct? Yes
Problem: The perimeter of a triangle is 923m. Two of its sides are 735m and 144m long respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 923 meters. - Two sides of the triangle have lengths of 735 meters and 144 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Side 1 + Side 2 + Side 3 923 = 735 + 144 + x Rearranging the terms, we get: x = 923 - 735 - 144 x = 44 meters Therefore, the length of the third side of the triangle is 44 meters. ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: An equilateral triangle has a perimeter of 813 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 813 cm. Step 1: Set up the equation using the given information. 813 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 813 / 3 side length = 271 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 813 cm is 271 cm. ### Answer: 271 cm
Expected answer: 271
Correct? Yes
Problem: An equilateral triangle has a perimeter of 834 feet. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 834 feet. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 834 feet = 3 × Side length Side length = 834 feet / 3 Side length = 278 feet Therefore, each side of the equilateral triangle has a length of 278 feet. ### Answer: 278
Expected answer: 278
Correct? Yes
Problem: A triangle has a perimeter of 105m and all its sides are equal in length. How long is one side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the given information and the properties of an equilateral triangle. Given information: - The perimeter of the triangle is 105 meters. - All sides of the triangle are equal in length. Properties of an equilateral triangle: - An equilateral triangle has three equal sides. - The sum of the lengths of the three sides is equal to the perimeter. Let's represent the length of one side as x. Since all sides are equal, we can write: x + x + x = 105 (Perimeter) 3x = 105 Dividing both sides by 3, we get: x = 105 / 3 x = 35 Therefore, the length of one side of the equilateral triangle is 35 meters. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: A triangle has a perimeter of 195cm. Given that all sides of the triangle are equal, what is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to use the given information and the properties of an equilateral triangle. Given information: - The perimeter of the triangle is 195 cm. - All sides of the triangle are equal (equilateral triangle). Properties of an equilateral triangle: - All three sides have equal lengths. - The perimeter of a triangle is the sum of the lengths of its three sides. Let's represent the length of each side as x. Since all sides are equal, we can write: x + x + x = 195 (Perimeter of the triangle) 3x = 195 Dividing both sides by 3, we get: x = 195 / 3 x = 65 Therefore, the length of each side of the equilateral triangle is 65 cm. ### Answer: 65
Expected answer: 65
Correct? Yes
Problem: A triangle has a perimeter of 919m. You know that one of its sides is 350m long and the other side is 154m long. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 919 meters. - One side of the triangle is 350 meters long. - Another side of the triangle is 154 meters long. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Side 1 + Side 2 + Side 3 919 = 350 + 154 + x Rearranging the terms, we get: x = 919 - 350 - 154 x = 415 meters Therefore, the length of the third side of the triangle is 415 meters. ### Answer: 415
Expected answer: 415
Correct? Yes
Problem: A triangle has a perimeter of 989m. You know that two of its sides are 128m and 288m long respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 989 meters. - The length of one side is 128 meters. - The length of another side is 288 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of the lengths of all three sides 989 = 128 + 288 + x Rearranging the terms, we get: x = 989 - 128 - 288 x = 573 meters Therefore, the length of the third side of the triangle is 573 meters. ### Answer: 573
Expected answer: 573
Correct? Yes
Problem: An equilateral triangle has a perimeter of 321 meters. If all sides are equal, what is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 321 meters. Let's represent the length of each side as x. Since the triangle is equilateral, we can write the perimeter as: Perimeter = x + x + x = 3x We know that the perimeter is 321 meters, so we can substitute this value into the equation: 321 = 3x Dividing both sides by 3, we get: x = 321 / 3 x = 107 Therefore, the length of each side of the equilateral triangle is 107 meters. ### Answer: 107
Expected answer: 107
Correct? Yes
Problem: An equilateral triangle has a perimeter of 258 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 258 cm. Step 1: Set up the equation using the given information. 258 cm = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 258 cm / 3 side length = 86 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 258 cm is 86 cm. ### Answer: 86 cm
Expected answer: 86
Correct? Yes
Problem: An equilateral triangle has a perimeter of 75m. What is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 75 meters. Step 1: Set up the equation using the given information. 75 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 75 / 3 side length = 25 meters Therefore, each side of the equilateral triangle has a length of 25 meters. ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: The perimeter of a triangle is 979m. Two of its sides are 620m and 80m respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 979 meters. - Two sides of the triangle have lengths of 620 meters and 80 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Side 1 + Side 2 + Side 3 979 = 620 + 80 + x Rearranging the terms: x = 979 - 620 - 80 x = 279 meters Therefore, the length of the third side of the triangle is 279 meters. ### Answer: 279
Expected answer: 279
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966 meters. What is the length of each side of this triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 966 meters. Step 1: Set up the equation using the given information. 966 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 966 / 3 side length = 322 meters Therefore, the length of each side of the equilateral triangle with a perimeter of 966 meters is 322 meters. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 486 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 486 cm. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 486 cm = 3 × Side length Side length = 486 cm / 3 Side length = 162 cm Therefore, each side of the equilateral triangle has a length of 162 cm. ### Answer: 162
Expected answer: 162
Correct? Yes
Problem: An equilateral triangle has a perimeter of 948 meters. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 948 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 948 meters = 3 × Side length Side length = 948 meters / 3 Side length = 316 meters Therefore, each side of the equilateral triangle has a length of 316 meters. ### Answer: 316
Expected answer: 316
Correct? Yes
Problem: A scalene triangle has three sides of different lengths. The first side is 252m, and the second side is 687m. The total perimeter of the triangle is 998m. Can you find the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the given information about the lengths of the first two sides and the total perimeter of the triangle. Given information: - The first side of the triangle is 252 meters. - The second side of the triangle is 687 meters. - The total perimeter of the triangle is 998 meters. Let's denote the length of the third side as x. Since the total perimeter is the sum of all three sides, we can write an equation: 252 + 687 + x = 998 Rearranging the terms, we get: x = 998 - 252 - 687 x = 59 meters Therefore, the length of the third side of the scalene triangle is 59 meters. ### Answer: 59
Expected answer: 59
Correct? Yes
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 618 meters. Step 1: Set up the equation using the given information. 618 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 618 / 3 side length = 206 Therefore, the length of each side of the equilateral triangle is 206 meters. ### Answer: 206
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 483 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 483 meters = 3 × Side length Side length = 483 meters / 3 Side length = 161 meters Therefore, each side of the equilateral triangle with a perimeter of 483 meters is 161 meters long. ### Answer: 161
Expected answer: 161
Correct? Yes
Problem: A triangle has a perimeter of 804m. One of its sides is 262m long and another is 90m long. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 804 meters. - One side of the triangle is 262 meters long. - Another side of the triangle is 90 meters long. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of the lengths of all three sides 804 = 262 + 90 + x Rearranging the equation to find x: x = 804 - 262 - 90 x = 452 Therefore, the length of the third side of the triangle is 452 meters. ### Answer: 452
Expected answer: 452
Correct? Yes
Problem: A large triangle has a perimeter of 925m. Two of its sides are 183m and 498m, respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 925 meters. - The length of one side is 183 meters. - The length of another side is 498 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Side 1 + Side 2 + Side 3 925 = 183 + 498 + x Rearranging the terms, we get: x = 925 - 183 - 498 x = 244 meters Therefore, the length of the third side of the triangle is 244 meters. ### Answer: 244
Expected answer: 244
Correct? Yes
Problem: A scalene triangle has a total perimeter of 573m. One of its sides measures 103m and another side measures 386m. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the property that the sum of the lengths of all sides in a triangle is equal to its perimeter. Given information: - The triangle is scalene (all sides have different lengths). - The total perimeter of the triangle is 573 meters. - One side measures 103 meters. - Another side measures 386 meters. Let's represent the length of the third side as x. We know that the sum of the lengths of all sides is equal to the perimeter. 103 + 386 + x = 573 Rearranging the terms, we get: x = 573 - 103 - 386 x = 84 Therefore, the length of the third side of the scalene triangle is 84 meters. ### Answer: 84
Expected answer: 84
Correct? Yes
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 330 meters. Step 1: Set up the equation using the given information. 330 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 330 / 3 side length = 110 meters Therefore, the length of each side of the equilateral triangle with a perimeter of 330 meters is 110 meters. ### Answer: 110
Expected answer: 110
Correct? Yes
Problem: A triangle has a perimeter of 850m. Two of its sides have lengths of 57m and 426m, respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 850 meters. - The length of one side is 57 meters. - The length of another side is 426 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of the lengths of all three sides 850 = 57 + 426 + x Rearranging the terms, we get: x = 850 - 57 - 426 x = 367 meters Therefore, the length of the third side of the triangle is 367 meters. ### Answer: 367
Expected answer: 367
Correct? Yes
Problem: A triangle has a perimeter of 764m. Two of its sides are 265m and 56m in length. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 764 meters. - The length of one side is 265 meters. - The length of another side is 56 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of the lengths of all three sides 764 = 265 + 56 + x Rearranging the equation to find x: x = 764 - 265 - 56 x = 443 meters Therefore, the length of the third side of the triangle is 443 meters. ### Answer: 443
Expected answer: 443
Correct? Yes
Problem: An equilateral triangle has a perimeter of 723cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 723 cm. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 723 cm = 3 × Side length Side length = 723 cm / 3 Side length = 241 cm Therefore, each side of the equilateral triangle has a length of 241 cm. ### Answer: 241
Expected answer: 241
Correct? Yes
Problem: A triangle has a side with a length of 315m and another side with a length of 100m. If the perimeter of the triangle is 738m, what is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - One side of the triangle has a length of 315 meters. - Another side of the triangle has a length of 100 meters. - The perimeter of the triangle is 738 meters. Let's represent the length of the third side as x. Perimeter of a triangle = Sum of the lengths of all three sides 738 meters = 315 meters + 100 meters + x Rearranging the equation, we get: x = 738 meters - 315 meters - 100 meters x = 323 meters Therefore, the length of the third side of the triangle is 323 meters. ### Answer: 323
Expected answer: 323
Correct? Yes
Problem: A triangle has a perimeter of 762m. If one of the sides measures 131m, and the other side is 147m long, what is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 762 meters. - One side of the triangle is 131 meters long. - Another side of the triangle is 147 meters long. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Side 1 + Side 2 + Side 3 762 = 131 + 147 + x Rearranging the terms, we get: x = 762 - 131 - 147 x = 484 Therefore, the length of the third side of the triangle is 484 meters. ### Answer: 484
Expected answer: 484
Correct? Yes
Problem: A triangle has a perimeter of 784m and you know the sum of two of its sides is 472m. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the properties of a triangle and the given information about the perimeter and the sum of two sides. Given information: - The perimeter of the triangle is 784 meters. - The sum of two sides of the triangle is 472 meters. Let's represent the three sides of the triangle as a, b, and c. Step 1: Express the perimeter in terms of the sides. Perimeter = a + b + c = 784 meters Step 2: Substitute the given information about the sum of two sides. a + b = 472 meters Step 3: Substitute the expression for (a + b) in the perimeter equation. Perimeter = a + b + c 784 = 472 + c c = 784 - 472 c = 312 meters Therefore, the length of the third side of the triangle is 312 meters. ### Answer: 312
Expected answer: 312
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543mm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 543 mm. Step 1: Set up the equation using the given information. 543 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 543 / 3 Side length = 181 mm Therefore, the length of each side of the equilateral triangle with a perimeter of 543 mm is 181 mm. ### Answer: 181 mm
Expected answer: 181
Correct? Yes
Problem: A triangle has a first side length of 287m, a second side length of 475m, and a perimeter of 867m. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - First side length = 287 meters - Second side length = 475 meters - Perimeter of the triangle = 867 meters Let's call the third side length x. Perimeter of a triangle = Sum of the lengths of all three sides 867 meters = 287 meters + 475 meters + x Rearranging the equation to isolate x: x = 867 meters - 287 meters - 475 meters x = 105 meters Therefore, the length of the third side of the triangle is 105 meters. ### Answer: 105
Expected answer: 105
Correct? Yes
Problem: The perimeter of a triangle is 934m. The lengths of two of its sides add up to 838m (one is 828m and the other is 10m). What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the properties of a triangle and the given information about the perimeter and the lengths of two sides. Given information: - The perimeter of the triangle is 934 meters. - The sum of the lengths of two sides is 838 meters (one side is 828 meters, and the other side is 10 meters). Step 1: Find the sum of the lengths of all three sides of the triangle. Perimeter of a triangle = Sum of the lengths of all three sides 934 meters = Length of side 1 + Length of side 2 + Length of side 3 Step 2: Substitute the known lengths of two sides. 934 meters = 828 meters + 10 meters + Length of side 3 Step 3: Solve for the length of the third side. Length of side 3 = 934 meters - 828 meters - 10 meters Length of side 3 = 96 meters Therefore, the length of the third side of the triangle is 96 meters. ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: A triangle has a perimeter of 677m. Two of its sides measure 109m and 530m respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 677 meters. - One side of the triangle measures 109 meters. - Another side of the triangle measures 530 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 677 = 109 + 530 + x Rearranging the terms, we get: x = 677 - 109 - 530 x = 38 meters Therefore, the length of the third side of the triangle is 38 meters. ### Answer: 38
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 582 cm. Step 1: Set up the equation using the given information. 582 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 582 / 3 Side length = 194 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 582 cm is 194 cm. ### Answer: 194
Expected answer: 194
Correct? Yes
Problem: A triangle has a perimeter of 499m. Its largest side is 259m long, and one of the other sides is 11m long. What is the length of the last side?
Claude-3 Sonnet:
To solve this problem, we need to use the properties of a triangle and the given information about the perimeter and the lengths of two sides. Given information: - The perimeter of the triangle is 499 meters. - The length of the largest side is 259 meters. - The length of one of the other sides is 11 meters. Step 1: Find the sum of the lengths of the two known sides. Sum of the known sides = 259 meters + 11 meters = 270 meters Step 2: Find the length of the unknown side using the property that the sum of the lengths of all sides is equal to the perimeter. Perimeter = Sum of the lengths of all sides 499 meters = 270 meters + Length of the unknown side Length of the unknown side = 499 meters - 270 meters Length of the unknown side = 229 meters Therefore, the length of the last side of the triangle is 229 meters. ### Answer: 229
Expected answer: 229
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 966 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 966 meters = 3 × Side length Side length = 966 meters / 3 Side length = 322 meters Therefore, each side of the equilateral triangle has a length of 322 meters. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 894 inches. What is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 894 inches. Step 1: Set up the equation using the given information. 894 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 894 / 3 Side length = 298 inches Therefore, the length of each side of the equilateral triangle with a perimeter of 894 inches is 298 inches. ### Answer: 298
Expected answer: 298
Correct? Yes
Problem: An equilateral triangle has a perimeter of 891cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 891 cm. Step 1: Set up the equation using the given information. 891 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 891 / 3 Side length = 297 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 891 cm is 297 cm. ### Answer: 297 cm
Expected answer: 297
Correct? Yes
Problem: A triangle has a perimeter of 762 meters. Two sides of these triangle are known to be 122 meters and 245 meters long respectively. Can you calculate the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 762 meters. - One side of the triangle is 122 meters long. - Another side of the triangle is 245 meters long. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of the lengths of all three sides 762 = 122 + 245 + x Rearranging the terms, we get: x = 762 - 122 - 245 x = 395 meters Therefore, the length of the third side of the triangle is 395 meters. ### Answer: 395
Expected answer: 395
Correct? Yes
Problem: An equilateral triangle has a perimeter of 411m. What is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 411 meters. Step 1: Set up the equation using the given information. 411 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 411 / 3 side length = 137 Therefore, the length of each side of the equilateral triangle is 137 meters. ### Answer: 137
Expected answer: 137
Correct? Yes
Problem: A triangle has three identical sides and the total length of the sides is 72m. What is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the property of an equilateral triangle, which states that all three sides are equal in length. Given information: - The triangle has three identical sides. - The total length of the sides is 72 meters. Let's represent the length of each side as x. Since all three sides are equal, we can write the equation: x + x + x = 72 Simplifying the equation: 3x = 72 Dividing both sides by 3: x = 72 / 3 x = 24 Therefore, the length of each side of the equilateral triangle is 24 meters. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: A large triangle has a perimeter of 930 meters. Two of its sides measure 537 meters and 68 meters respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 930 meters. - One side of the triangle measures 537 meters. - Another side of the triangle measures 68 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 930 = 537 + 68 + x Rearranging the terms, we get: x = 930 - 537 - 68 x = 325 meters Therefore, the length of the third side of the triangle is 325 meters. ### Answer: 325
Expected answer: 325
Correct? Yes
Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 657 meters. Step 1: Set up the equation using the given information. 657 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 657 / 3 side length = 219 Therefore, the length of each side of the equilateral triangle is 219 meters. ### Answer: 219
Expected answer: 219
Correct? Yes
Problem: A scalene triangle has a side that measures 368m and another side that measures 230m. If the perimeter of the triangle is 909m, what is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of the third side of the scalene triangle using the given information about the other two sides and the perimeter. Given information: - One side of the triangle measures 368 meters. - Another side of the triangle measures 230 meters. - The perimeter of the triangle is 909 meters. Step 1: Find the sum of the known sides. Sum of the known sides = 368 meters + 230 meters = 598 meters Step 2: Find the length of the third side by subtracting the sum of the known sides from the perimeter. Length of the third side = Perimeter - Sum of the known sides Length of the third side = 909 meters - 598 meters = 311 meters Therefore, the length of the third side of the scalene triangle is 311 meters. ### Answer: 311
Expected answer: 311
Correct? Yes
Problem: A triangle has a perimeter of 700 m. Two of its sides are 140m and 525m long. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 700 m. - Two sides of the triangle have lengths of 140 m and 525 m. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 700 m = 140 m + 525 m + x Rearranging the terms, we get: x = 700 m - 140 m - 525 m x = 35 m Therefore, the length of the third side of the triangle is 35 m. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: A triangle has a perimeter of 915cm. Two of its sides are 484cm and 130cm respectively. What length is the third side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 915 cm. - One side of the triangle is 484 cm. - Another side of the triangle is 130 cm. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 915 cm = 484 cm + 130 cm + x Rearranging the terms, we get: x = 915 cm - 484 cm - 130 cm x = 301 cm Therefore, the length of the third side of the triangle is 301 cm. ### Answer: 301
Expected answer: 301
Correct? Yes
Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the given information about the perimeter of the equilateral triangle and the fact that all sides of an equilateral triangle are equal in length. Given information: - The triangle is equilateral, which means all sides have equal length. - The perimeter of the triangle is 120 cm. Step 1: Find the length of one side of the triangle. Perimeter of a triangle = Sum of the lengths of all three sides 120 cm = Side 1 + Side 2 + Side 3 Since all sides are equal in an equilateral triangle, let's represent the length of each side as x. 120 cm = x + x + x 120 cm = 3x x = 120 cm / 3 x = 40 cm Therefore, each side of the equilateral triangle has a length of 40 cm. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A triangular field has a perimeter of 661m. Two sides of the field are known to be 382m and 151m respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangular field is 661 meters. - Two sides of the field are 382 meters and 151 meters. Let's represent the length of the third side as x. According to the perimeter formula for a triangle: Perimeter = Side 1 + Side 2 + Side 3 661 = 382 + 151 + x Rearranging the terms, we get: x = 661 - 382 - 151 x = 128 meters Therefore, the length of the third side of the triangular field is 128 meters. ### Answer: 128
Expected answer: 128
Correct? Yes
Problem: A triangle has a total perimeter of 678 feet. Two of its sides measure 419 feet and 164 feet respectively. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the property that the sum of the lengths of all sides of a triangle is equal to its perimeter. Given information: - The total perimeter of the triangle is 678 feet. - One side of the triangle measures 419 feet. - Another side of the triangle measures 164 feet. Let's represent the length of the third side as x. According to the property of the perimeter of a triangle, we can write: 419 + 164 + x = 678 Rearranging the terms, we get: x = 678 - 419 - 164 x = 95 Therefore, the length of the third side of the triangle is 95 feet. ### Answer: 95
Expected answer: 95
Correct? Yes
Problem: The perimeter of a triangle is 248m. Two of the sides are 186m and 37m long, respectively. What is the length of the remaining side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 248 meters. - One side of the triangle is 186 meters long. - Another side of the triangle is 37 meters long. Let's represent the length of the remaining side as x. According to the perimeter formula: Perimeter = Sum of all three sides 248 = 186 + 37 + x Rearranging the terms, we get: x = 248 - 186 - 37 x = 25 meters Therefore, the length of the remaining side of the triangle is 25 meters. ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: An equilateral triangle has a perimeter of 246 centimeters. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 246 centimeters. Step 1: Set up the equation using the given information. 246 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 246 / 3 side length = 82 Therefore, the length of each side of the equilateral triangle is 82 centimeters. ### Answer: 82
Expected answer: 82
Correct? Yes
Problem: The total perimeter of a triangular field is 739 meters. Two of its sides measure 180 meters and 338 meters respectively. Find the length of the third side.
Claude-3 Sonnet:
To solve this problem, we need to use the properties of triangles and the formula for the perimeter of a triangle. Given information: - The total perimeter of the triangular field is 739 meters. - Two sides of the triangle measure 180 meters and 338 meters. Let's denote the length of the third side as x. According to the formula for the perimeter of a triangle: Perimeter = Sum of the lengths of all three sides 739 = 180 + 338 + x 739 = 518 + x x = 739 - 518 x = 221 meters Therefore, the length of the third side of the triangular field is 221 meters. ### Answer: 221
Expected answer: 221
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 684 cm. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 684 cm = 3 × Side length Side length = 684 cm / 3 Side length = 228 cm Therefore, each side of the equilateral triangle has a length of 228 cm. ### Answer: 228
Expected answer: 228
Correct? Yes
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 537 meters. Step 1: Set up the equation using the given information. 537 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 537 / 3 side length = 179 Therefore, the length of each side of the equilateral triangle is 179 meters. ### Answer: 179
Expected answer: 179
Correct? Yes
Problem: A triangle has a perimeter of 568m. The lengths of two of its sides are 110m and 205m. What is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - The perimeter of the triangle is 568 meters. - The lengths of two sides are 110 meters and 205 meters. Let's represent the length of the third side as x. According to the perimeter formula: Perimeter = Sum of all three sides 568 = 110 + 205 + x Rearranging the equation: x = 568 - 110 - 205 x = 253 meters Therefore, the length of the third side of the triangle is 253 meters. ### Answer: 253
Expected answer: 253
Correct? Yes
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 942 mm. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 942 mm = 3 × Side length Side length = 942 mm / 3 Side length = 314 mm Therefore, each side of the equilateral triangle has a length of 314 mm. ### Answer: 314
Expected answer: 314
Correct? Yes
Problem: A triangular garden has one side that is 325 meters long and another that is 15 meters long. The total perimeter of the triangle is 633 meters. What is the length of the third side of the garden?
Claude-3 Sonnet:
To solve this problem, we need to use the given information about the lengths of two sides and the total perimeter of the triangle to find the length of the third side. Given information: - One side of the triangle is 325 meters long. - Another side of the triangle is 15 meters long. - The total perimeter of the triangle is 633 meters. Let's denote the length of the third side as x. Step 1: Write an equation for the perimeter of the triangle. Perimeter of a triangle = Sum of the lengths of all three sides 633 = 325 + 15 + x Step 2: Solve the equation for x. 633 = 325 + 15 + x 633 - 325 - 15 = x 293 = x Therefore, the length of the third side of the garden is 293 meters. ### Answer: 293
Expected answer: 293
Correct? Yes
Problem: An equilateral triangle has a perimeter of 504 meters. What is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the given information about the perimeter of the equilateral triangle and the fact that all sides of an equilateral triangle are equal in length. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 504 meters. Step 1: Find the length of one side of the triangle. Perimeter of a triangle = Sum of the lengths of all three sides 504 meters = Side length + Side length + Side length 504 meters = 3 × Side length Side length = 504 meters / 3 Side length = 168 meters Therefore, each side of the equilateral triangle has a length of 168 meters. ### Answer: 168 meters
Expected answer: 168
Correct? Yes
Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is given by: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 51 cm. Step 1: Set up the equation using the given information. 51 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 51 / 3 side length = 17 Therefore, the length of each side of the equilateral triangle with a perimeter of 51 cm is 17 cm. ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: An equilateral triangle has a perimeter of 501 feet. What is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 501 feet. Step 1: Set up the equation using the given information. 501 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 501 / 3 side length = 167 Therefore, the length of each side of the equilateral triangle is 167 feet. ### Answer: 167
Expected answer: 167
Correct? Yes
Problem: The perimeter of an equilateral triangle is 411 meters. What is the length of each side of the triangle?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is given by: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 411 meters. Step 1: Set up the equation using the given information. 411 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 411 / 3 side length = 137 Therefore, the length of each side of the equilateral triangle is 137 meters. ### Answer: 137
Expected answer: 137
Correct? Yes
Problem: An equilateral triangle has a perimeter of 114cm. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 114 cm. Step 1: Set up the equation using the given information. 114 cm = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. Side length = 114 cm / 3 Side length = 38 cm Therefore, the length of each side of the equilateral triangle with a perimeter of 114 cm is 38 cm. ### Answer: 38
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of an equilateral triangle, which is given by: Perimeter = 3 × side length Given information: - The perimeter of the equilateral triangle is 69 meters. Step 1: Set up the equation using the given information. 69 = 3 × side length Step 2: Divide both sides of the equation by 3 to find the side length. side length = 69 / 3 side length = 23 meters Therefore, the length of each side of the equilateral triangle with a perimeter of 69 meters is 23 meters. ### Answer: 23
Expected answer: 23
Correct? Yes
Problem: A triangle has sides of lengths 464m and 377m respectively. If the total perimeter of the triangle is 907m, what is the length of the third side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given information: - One side of the triangle has a length of 464 meters. - Another side of the triangle has a length of 377 meters. - The total perimeter of the triangle is 907 meters. Let's denote the length of the third side as x. According to the perimeter formula, we have: Perimeter = Sum of the lengths of all three sides 907 = 464 + 377 + x Rearranging the terms, we get: x = 907 - 464 - 377 x = 66 Therefore, the length of the third side of the triangle is 66 meters. ### Answer: 66
Expected answer: 66
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the length of each side of the equilateral triangle given its perimeter. Given information: - The triangle is equilateral, which means all sides have equal lengths. - The perimeter of the triangle is 966 meters. Step 1: Find the relationship between the perimeter and the side lengths of an equilateral triangle. Perimeter of an equilateral triangle = Sum of the lengths of all three sides Perimeter = Side length + Side length + Side length Perimeter = 3 × Side length Step 2: Substitute the given perimeter value and solve for the side length. 966 meters = 3 × Side length Side length = 966 meters / 3 Side length = 322 meters Therefore, each side of the equilateral triangle has a length of 322 meters. ### Answer: 322
Expected answer: 322
Correct? Yes