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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 990cm, so we can set up the equation: 3x = 990 To solve for x, we can divide both sides of the equation by 3: x = 990/3 x = 330 So, the length of each side of the equilateral triangle is 330cm. ### Answer: 330
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 997m, and we know two of the sides have lengths 2m and 667m. So, we can set up the equation: 997 = 2 + 667 + c Subtract 2 and 667 from both sides: 997 - 2 - 667 = c c = 328 So, the length of the third side is 328m. ### Answer: 328m
Expected answer: 328
Correct? Yes
Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 579 cm, so we can set up the equation: 3x = 579 To solve for x, we can divide both sides of the equation by 3: x = 579 รท 3 x = 193 So, the length of each side of the equilateral triangle is 193 cm. ### Answer: 193
Expected answer: 193
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 684m, so we can set up the equation: 3x = 684 To solve for x, we can divide both sides of the equation by 3: x = 684 รท 3 x = 228 So, the length of each side of the equilateral triangle is 228m. ### 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 503 meters, and we know two of the sides are 223 meters and 46 meters long. We can set up an equation: 223 + 46 + c = 503 Combine like terms: 269 + c = 503 Subtract 269 from both sides: c = 234 So, the length of the remaining side 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?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all sides are equal. Let's call the length of each side "x". The perimeter is the sum of all sides, so we can set up the equation: x + x + x = 105 Combine like terms: 3x = 105 Divide both sides by 3: x = 35 So, the length of each side is 35m. ### Answer: 35m
Expected answer: 35
Correct? Yes
Problem: An equilateral triangle has a perimeter of 306cm. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 306cm, so we can set up the equation: 3x = 306 To solve for x, we can divide both sides of the equation by 3: x = 306 รท 3 x = 102 So, the length of each side of the equilateral triangle is 102cm. ### 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?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation: x + x + x = 33 Combine like terms: 3x = 33 Divide both sides by 3: x = 11 So, the length of each side is 11 cm. ### Answer: 11
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 861m, and we know two of the sides are 192m and 159m. We can set up an equation: 192 + 159 + c = 861 Combine like terms: 351 + c = 861 Subtract 351 from both sides: c = 510 So, the length of the third side is 510m. ### Answer: 510m
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?
Llama 3 8B:
Reasoning: Let's call the length of one side "x". Since the perimeter is the sum of all sides, we can set up the equation: x + x + x = 489 Combine like terms: 3x = 489 Divide both sides by 3: x = 489/3 x = 163 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter of the triangle is the sum of all its sides, which is 3x. We are given that the perimeter is 696 meters, so we can set up the equation: 3x = 696 To solve for x, we can divide both sides of the equation by 3: x = 696 รท 3 x = 232 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". The perimeter of a triangle is the sum of the lengths of all its sides, so we can set up the equation: 180 + 579 + x = 804 To solve for x, we can subtract 180 and 579 from both sides of the equation: x = 804 - 180 - 579 x = 45 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 915cm, so we can set up the equation: 3x = 915 To solve for x, we can divide both sides of the equation by 3: x = 915 รท 3 x = 305 So, the length of each side of the equilateral triangle is 305cm. ### Answer: 305cm
Expected answer: 305
Correct? Yes
Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 564 cm, so we can set up the equation: 3x = 564 To solve for x, we can divide both sides of the equation by 3: x = 564 รท 3 x = 188 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 594 cm, so we can set up the equation: 3x = 594 To solve for x, we can divide both sides of the equation by 3: x = 594 รท 3 x = 198 So, the length of each side of the equilateral triangle is 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 453 cm, so we can set up the equation: 3x = 453 To solve for x, we can divide both sides by 3: x = 453 รท 3 x = 151 So, each side of the triangle is 151 cm long. ### 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the total perimeter is 898m, and we know the lengths of two of the sides (250m and 435m). We can set up an equation: 250 + 435 + c = 898 Combine like terms: 685 + c = 898 Subtract 685 from both sides: c = 213 So, the length of the third side of the triangle is 213m. ### Answer: 213m
Expected answer: 213
Correct? Yes
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation: 3x = 405 To find the length of each side, we can divide both sides by 3: x = 405 รท 3 x = 135 So, 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?
Llama 3 8B:
Reasoning: Since the space is an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We know that the perimeter is 612 meters, so we can set up the equation: 3x = 612 To solve for x, we can divide both sides of the equation by 3: x = 612 รท 3 x = 204 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides are equal. The perimeter of the triangle is the sum of all three sides, which is 591 cm. We can set up an equation: x + x + x = 591 Combine like terms: 3x = 591 Divide both sides by 3: x = 197 So, the length of each side of the equilateral triangle is 197 cm. ### Answer: 197
Expected answer: 197
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 858m, so we can set up the equation: 3x = 858 To solve for x, we can divide both sides of the equation by 3: x = 858 รท 3 x = 286 So, the length of each side of the equilateral triangle is 286m. ### Answer: 286m
Expected answer: 286
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543 meters. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 543 meters, so we can set up the equation: 3x = 543 To solve for x, we can divide both sides of the equation by 3: x = 543 รท 3 x = 181 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Reasoning: Since the triangle has three equal sides, we can let the length of each side be x. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 255 meters, so we can set up the equation 3x = 255. To solve for x, we can divide both sides of the equation by 3, which gives us x = 255/3. x = 85. ### 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.
Llama 3 8B:
Reasoning: Since the triangle is equilateral, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 570mm, so we can set up the equation: 3x = 570 To solve for x, we can divide both sides of the equation by 3: x = 570 รท 3 x = 190 So, the length of each side of the equilateral triangle is 190mm. ### Answer: 190mm
Expected answer: 190
Correct? Yes
Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all sides are equal. Let's call the length of each side "x". The perimeter is the sum of all sides, so we can set up the equation: x + x + x = 129 Combine like terms: 3x = 129 Divide both sides by 3: x = 129/3 x = 43 So, the length of each side is 43m. ### Answer: 43m
Expected answer: 43
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858 meters. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 858 meters, so we can set up the equation: 3x = 858 To solve for x, we can divide both sides of the equation by 3: x = 858 รท 3 x = 286 So, 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?
Llama 3 8B:
Reasoning: Since the triangle is equilateral, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 513 km. We can set up an equation: x + x + x = 513 Combine like terms: 3x = 513 Divide both sides by 3: x = 171 So, each side of the triangle is 171 km long. ### Answer: 171 km
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 828 meters, and we know two of the sides are 105 and 434 meters long. We can set up an equation: 105 + 434 + c = 828 Combine like terms: 539 + c = 828 Subtract 539 from both sides: c = 828 - 539 c = 289 So, the third side of the field is 289 meters long. ### 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?
Llama 3 8B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all its sides. Let's denote the length of the third side as x. We can set up the equation: 37 + 559 + x = 773 Simplifying the equation, we get: 596 + x = 773 Subtracting 596 from both sides, we get: x = 177 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 714m, so we can set up the equation: 3x = 714 To solve for x, we can divide both sides of the equation by 3: x = 714 รท 3 x = 238 So, the length of each side of the equilateral triangle is 238m. ### Answer: 238m
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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". Since it's a triangle, the perimeter is the sum of all three sides, which is 792m. We can set up an equation: 147 + 590 + x = 792 Combine like terms: 737 + x = 792 Subtract 737 from both sides: x = 55 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". The perimeter of a triangle is the sum of the lengths of all its sides, so we can set up the equation: 321 + 528 + x = 871 To solve for x, we can subtract 321 and 528 from both sides of the equation: x = 871 - 321 - 528 x = 22 ### 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.
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We are given that the perimeter is 991m, and two of the sides are 424m and 246m. We can set up an equation: 424 + 246 + c = 991 Combine like terms: 670 + c = 991 Subtract 670 from both sides: c = 991 - 670 c = 321 So, the length of the third side of the triangle is 321m. ### Answer: 321m.
Expected answer: 321
Correct? Yes
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 936m, so we can set up the equation: 3x = 936 To solve for x, we can divide both sides by 3: x = 936 รท 3 x = 312 So, each side of the triangle is 312m 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?
Llama 3 8B:
Reasoning: Let the length of the third side be x. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 721m. We can set up an equation using the given information: 204 + 195 + x = 721 Simplifying the equation, we get: 399 + x = 721 Subtracting 399 from both sides gives: x = 722 - 399 x = 323 ### Answer: 323m
Expected answer: 322
Correct? No
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 201m, so we can set up the equation: 3x = 201 To solve for x, we can divide both sides of the equation by 3: x = 201/3 x = 67 So, the length of each side of the equilateral triangle is 67m. ### 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.
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation: 3x = 756 To find the length of each side, we can divide both sides of the equation by 3: x = 756 รท 3 x = 252 So, the length of each side of the equilateral triangle is 252m. ### Answer: 252
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?
Llama 3 8B:
Reasoning: Let the length of the third side be x. The perimeter of a triangle is the sum of the lengths of all its sides. So, we can set up the equation: 735 + 144 + x = 923 Subtracting 735 and 144 from both sides gives: x = 44 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 813 cm, so we can set up the equation: 3x = 813 To solve for x, we can divide both sides of the equation by 3: x = 813 รท 3 x = 271 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 834 feet, so we can set up the equation: 3x = 834 To solve for x, we can divide both sides of the equation by 3: x = 834 รท 3 x = 278 So, the length of each side of the equilateral triangle is 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?
Llama 3 8B:
Reasoning: Since the perimeter of the triangle is 105m, and all sides are equal, we can divide the perimeter by 3 to find the length of one side. 105m รท 3 = 35m ### Answer: 35m
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?
Llama 3 8B:
Reasoning: Since the perimeter of the triangle is 195cm, and all sides are equal, we can divide the perimeter by 3 to find the length of each side. Perimeter = 195cm Length of each side = Perimeter รท 3 = 195cm รท 3 = 65cm ### Answer: 65cm
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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". Since the perimeter is the sum of all three sides, we can set up the equation: 350 + 154 + x = 919 Combine like terms: 504 + x = 919 Subtract 504 from both sides: x = 415 ### 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 989m, and we know two of the sides are 128m and 288m long. So, we can set up the equation: 128 + 288 + c = 989 Combine like terms: 416 + c = 989 Subtract 416 from both sides: c = 989 - 416 c = 573 So, the length of the third side is 573m. ### Answer: 573m.
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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal, so the perimeter is 3x. We know the perimeter is 321 meters, so we can set up the equation: 3x = 321. To solve for x, we can divide both sides by 3: x = 321/3. x = 107. ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 258 cm, so we can set up the equation: 3x = 258 To solve for x, we can divide both sides of the equation by 3: x = 258 รท 3 x = 86 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Reasoning: Since the triangle is equilateral, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 75m, so we can set up the equation: 3x = 75 To solve for x, we can divide both sides by 3: x = 75/3 x = 25 So, the length of each side of the triangle is 25m. ### Answer: 25m
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?
Llama 3 8B:
Reasoning: Let the length of the third side be x. The perimeter of a triangle is the sum of the lengths of all its sides. Therefore, we can set up the equation: 620 + 80 + x = 979 Simplifying the equation, we get: 700 + x = 979 Subtracting 700 from both sides, we get: x = 979 - 700 x = 279 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter of the triangle is the sum of all its sides, which is 3x. We are given that the perimeter is 966 meters, so we can set up the equation: 3x = 966 To solve for x, we can divide both sides of the equation by 3: x = 966 รท 3 x = 322 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 486 cm, so we can set up the equation: 3x = 486 To solve for x, we can divide both sides of the equation by 3: x = 486 รท 3 x = 162 So, the length of each side of the equilateral triangle is 162 cm. ### Answer: 162 cm.
Expected answer: 162
Correct? Yes
Problem: An equilateral triangle has a perimeter of 948 meters. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 948 meters, so we can set up the equation: 3x = 948 To solve for x, we can divide both sides of the equation by 3: x = 948 รท 3 x = 316 So, the length of each side of the equilateral triangle is 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?
Llama 3 8B:
Let's call the length of the third side "x". Since it's a scalene triangle, the three sides have different lengths, so we can't use any of the special triangle formulas that rely on equal sides. Instead, we can use the fact that the perimeter of the triangle is the sum of the lengths of all three sides. We know the perimeter is 998m, and we know two of the sides are 252m and 687m. So, we can set up the equation: 252 + 687 + x = 998 To solve for x, we can subtract 252 and 687 from both sides of the equation: x = 998 - 252 - 687 x = 59 So, the length of the third side is 59m. ### Answer: 59m.
Expected answer: 59
Correct? Yes
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 618m, so we can set up the equation: 3x = 618 To solve for x, we can divide both sides of the equation by 3: x = 618 รท 3 x = 206 So, the length of each side of the equilateral triangle is 206m. ### Answer: 206m
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
Llama 3 8B:
Reasoning: Let's call the length of each side "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 483 meters, so we can set up the equation: 3x = 483 To solve for x, we can divide both sides by 3: x = 483 รท 3 x = 161 So, each side of the equilateral triangle 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 804m, and we know two of the sides are 262m and 90m. We can plug these values into the formula: 804 = 262 + 90 + c First, let's add 262 and 90: 804 = 352 + c Now, subtract 352 from both sides: 804 - 352 = c 452 = c So, the length of the third side is 452m. ### 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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". We can use the formula for the perimeter of a triangle to set up an equation: 183 + 498 + x = 925 Combine like terms: 681 + x = 925 Subtract 681 from both sides: x = 244 ### 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?
Llama 3 8B:
Let's call the length of the third side "x". Since it's a scalene triangle, all sides are unequal. We can use the fact that the perimeter is the sum of all sides to set up an equation: 103 + 386 + x = 573 Combine like terms: 489 + x = 573 Subtract 489 from both sides: x = 84 So, the length of the third side is 84m. ### Answer: 84m
Expected answer: 84
Correct? Yes
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation: x + x + x = 330 Combine like terms: 3x = 330 Divide both sides by 3: x = 330/3 x = 110 So, the length of each side is 110m. ### 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 850m, and we know two of the sides have lengths 57m and 426m. So, we can set up the equation: 850 = 57 + 426 + c Now, we can simplify the equation by combining the known side lengths: 850 = 483 + c Subtract 483 from both sides to get: 367 = c So, the length of the third side is 367m. ### Answer: 367m.
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 764m, and we know two of the sides are 265m and 56m. So, we can set up the equation: 265 + 56 + c = 764 Combine like terms: 321 + c = 764 Subtract 321 from both sides: c = 443 So, the length of the third side is 443m. ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 723cm, so we can set up the equation: 3x = 723 To solve for x, we can divide both sides of the equation by 3: x = 723 รท 3 x = 241 So, the length of each side of the equilateral triangle is 241cm. ### Answer: 241cm
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a and b are the given side lengths, and c is the length of the third side. We know the perimeter is 738m, and we know the lengths of two sides: a = 315m b = 100m Perimeter = 738m We can set up an equation: 315 + 100 + c = 738 Now, let's simplify the equation: 415 + c = 738 Subtract 415 from both sides: c = 738 - 415 c = 323 So, the length of the third side is 323m. ### Answer: 323m
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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". Since the perimeter is the sum of all three sides, we can set up the equation: 131 + 147 + x = 762 Combine like terms: 278 + x = 762 Subtract 278 from both sides: x = 484 ### 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?
Llama 3 8B:
Let's say the length of the third side is x. We know that the sum of two sides is 472m, so we can set up the equation: a + b = 472 We also know that the perimeter is 784m, so we can set up the equation: a + b + x = 784 Subtracting the first equation from the second equation, we get: x = 784 - 472 x = 312 So, the length of the third side is 312m. ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 543mm, so we can set up the equation: 3x = 543 To solve for x, we can divide both sides of the equation by 3: x = 543 รท 3 x = 181 So, the length of each side of the equilateral triangle is 181mm. ### Answer: 181mm
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?
Llama 3 8B:
Reasoning: Let's denote the length of the third side as x. Since the perimeter is the sum of all three sides, we can set up the equation: 287 + 475 + x = 867 Subtracting 287 and 475 from both sides gives: x = 867 - 287 - 475 x = 105 ### Answer: 105m
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?
Llama 3 8B:
Let's use the information given to find the length of the third side. The perimeter of the triangle is 934m, which means the sum of the lengths of all three sides is 934m. We know the lengths of two sides: one is 828m and the other is 10m. Let's add these two lengths together: 828m + 10m = 838m This is equal to the sum of the lengths of the two sides mentioned in the problem, which is 838m. Now, we can set up an equation: 828m + 10m + x = 934m where x is the length of the third side. Combine like terms: 838m + x = 934m Subtract 838m from both sides: x = 934m - 838m x = 96m So, the length of the third side is 96m. ### Answer: 96m.
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 677m, and we know two of the sides are 109m and 530m. So, we can set up the equation: 677 = 109 + 530 + c Now, we can simplify the equation by combining the known sides: 677 = 639 + c Subtract 639 from both sides to get: 38 = c So, the length of the third side is 38m. ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 582 cm, so we can set up the equation: 3x = 582 To solve for x, we can divide both sides of the equation by 3: x = 582 รท 3 x = 194 So, the length of each side of the equilateral triangle 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 499m, and we know two of the sides: 259m and 11m. Let's call the length of the third side "x". We can set up an equation: 259 + 11 + x = 499 Combine like terms: 270 + x = 499 Subtract 270 from both sides: x = 229 So, the length of the last side is 229m. ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 966m, so we can set up the equation: 3x = 966 To solve for x, we can divide both sides of the equation by 3: x = 966 รท 3 x = 322 So, the length of each side of the equilateral triangle is 322m. ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 894 inches, so we can set up the equation: 3x = 894 To solve for x, we can divide both sides by 3: x = 894 รท 3 x = 298 So, the length of each side of the triangle 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 891cm, so we can set up the equation: 3x = 891 To solve for x, we can divide both sides of the equation by 3: x = 891 รท 3 x = 297 So, the length of each side of the equilateral triangle is 297cm. ### Answer: 297cm
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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". We can use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Since we know the perimeter is 762 meters, we can set up the equation: 122 + 245 + x = 762 Subtracting 122 and 245 from both sides gives us: x = 395 So, the length of the third side 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 411m, so we can set up the equation: 3x = 411 To solve for x, we can divide both sides by 3: x = 411/3 x = 137 So, the length of each side of the triangle is 137m. ### 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?
Llama 3 8B:
Reasoning: Since the triangle has three identical sides, the length of each side is the same. Let's call this length "x". The total length of the sides is 72m, so we can set up the equation: 3x = 72 To find the length of each side, we can divide both sides of the equation by 3: x = 72/3 x = 24 ### Answer: 24m
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 930 meters, and we know two of the sides are 537 meters and 68 meters. We can plug these values into the formula: 930 = 537 + 68 + c First, let's add the known sides: 930 = 605 + c Now, subtract 605 from both sides: 930 - 605 = c c = 325 So, the length of the third side 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 657 meters, so we can set up the equation: 3x = 657 To solve for x, we can divide both sides of the equation by 3: x = 657 รท 3 x = 219 So, 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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". Since it's a scalene triangle, all sides are different. We can set up an equation using the formula for the perimeter of a triangle: P = a + b + c where P is the perimeter, and a, b, and c are the lengths of the sides. We know the perimeter is 909m, and we know two of the sides are 368m and 230m. So, we can plug in the values: 909 = 368 + 230 + x Simplifying the equation, we get: 909 = 598 + x Subtracting 598 from both sides gives us: 311 = x So, the length of the third side is 311m. ### Answer: 311m.
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 700m, and we know two of the sides are 140m and 525m long. So, we can set up the equation: 700 = 140 + 525 + c Now, we can simplify the equation by combining the constants: 700 = 665 + c Subtract 665 from both sides: 35 = c So, the length of the third side is 35m. ### 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 915cm, and we know two of the sides are 484cm and 130cm. So, we can set up the equation: 915 = 484 + 130 + c Now, we can solve for c: 915 = 614 + c Subtract 614 from both sides: 301 = c So, the length of the third side of the triangle is 301cm. ### Answer: 301cm.
Expected answer: 301
Correct? Yes
Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 120 cm. We can set up an equation: x + x + x = 120 Combine like terms: 3x = 120 Divide both sides by 3: x = 40 So, each side of the triangle is 40 cm long. ### Answer: 40 cm
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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 661m, and we know two of the sides are 382m and 151m. We can set up an equation: 382 + 151 + c = 661 Combine like terms: 533 + c = 661 Subtract 533 from both sides: c = 128 So, the length of the third side is 128m. ### 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the total perimeter is 678 feet, and we know the lengths of two of the sides: 419 feet and 164 feet. We can set up an equation: 419 + 164 + c = 678 To solve for c, we can subtract 419 and 164 from both sides: c = 678 - 419 - 164 c = 95 So, the length of the third side 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?
Llama 3 8B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all its sides. Let's denote the length of the remaining side as x. We can set up the equation: 186 + 37 + x = 248 To solve for x, we can subtract 186 and 37 from both sides: x = 248 - 186 - 37 x = 25 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 246 centimeters, so we can set up the equation: 3x = 246 To solve for x, we can divide both sides of the equation by 3: x = 246 รท 3 x = 82 So, 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.
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the total perimeter is 739 meters, and we know two of the sides are 180 meters and 338 meters. We can set up an equation: 180 + 338 + c = 739 Combine like terms: 518 + c = 739 Subtract 518 from both sides: c = 221 So, the length of the third side 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?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation: 3x = 684 To find the length of each side, we can divide both sides by 3: x = 684 รท 3 x = 228 ### Answer: 228cm
Expected answer: 228
Correct? Yes
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 537m, so we can set up the equation: 3x = 537 To solve for x, we can divide both sides of the equation by 3: x = 537 รท 3 x = 179 So, the length of each side of the equilateral triangle is 179m. ### 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?
Llama 3 8B:
Let's use the formula for the perimeter of a triangle: Perimeter = a + b + c where a, b, and c are the lengths of the three sides. We know the perimeter is 568m, and we know the lengths of two of the sides: 110m and 205m. We can set up an equation: 110 + 205 + c = 568 Combine like terms: 315 + c = 568 Subtract 315 from both sides: c = 253 So, the length of the third side is 253m. ### Answer: 253m
Expected answer: 253
Correct? Yes
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 942mm, so we can set up the equation: 3x = 942 To solve for x, we can divide both sides of the equation by 3: x = 942 รท 3 x = 314 So, the length of each side of the equilateral triangle is 314mm. ### Answer: 314mm
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?
Llama 3 8B:
Reasoning: Let's call the length of the third side "x". The perimeter of the triangle is the sum of all its sides, which is 633 meters. We know that one side is 325 meters and another is 15 meters, so we can set up the equation: 325 + 15 + x = 633 Simplifying the equation, we get: 340 + x = 633 Subtracting 340 from both sides gives us: x = 293 ### 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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 504 meters, so we can set up the equation: 3x = 504 To solve for x, we can divide both sides by 3: x = 504 / 3 x = 168 So, the length of each side of the triangle is 168 meters. ### Answer: 168
Expected answer: 168
Correct? Yes
Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all sides are equal. Let's call the length of each side "x". The perimeter is the sum of all sides, so we can set up the equation: x + x + x = 51 Combine like terms: 3x = 51 Divide both sides by 3: x = 17 So, the length of each side is 17 cm. ### Answer: 17 cm.
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?
Llama 3 8B:
Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 501 feet, so we can set up the equation: 3x = 501 To solve for x, we can divide both sides by 3: x = 501/3 x = 167 So, the length of each side of the 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?
Llama 3 8B:
Reasoning: The perimeter of an equilateral triangle is the sum of the lengths of all its sides. Since it is an equilateral triangle, all its sides are equal. Let's call the length of each side "x". Then, the perimeter is 3x. We know that the perimeter is 411 meters, so we can set up the equation: 3x = 411 To solve for x, we can divide both sides by 3: x = 411 / 3 x = 137 So, the length of each side of the 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?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation: x + x + x = 114 Combine like terms: 3x = 114 Divide both sides by 3: x = 38 So, the length of each side is 38cm. ### Answer: 38cm
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation: x + x + x = 69 Combine like terms: 3x = 69 Divide both sides by 3: x = 69/3 x = 23 So, the length of each side is 23m. ### Answer: 23m
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?
Llama 3 8B:
Let's denote the length of the third side as x. We know that the total perimeter of the triangle is 907m, which is the sum of the lengths of all three sides. Therefore, we can set up the equation: 464 + 377 + x = 907 Combine like terms: 841 + x = 907 Subtract 841 from both sides: x = 907 - 841 x = 66 So, the length of the third side is 66m. ### Answer: 66m.
Expected answer: 66
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Llama 3 8B:
Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x. We are given that the perimeter is 966m, so we can set up the equation: 3x = 966 To solve for x, we can divide both sides of the equation by 3: x = 966 รท 3 x = 322 So, the length of each side of the equilateral triangle is 322m. ### Answer: 322m
Expected answer: 322
Correct? Yes