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 70B:
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 990cm. We can set up the equation: x + x + x = 990. Combine like terms: 3x = 990. Divide both sides by 3: x = 990/3. x = 330. ### Answer: 330cm.
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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 2 + 667 + x = 997 To solve for x, we can subtract 2 and 667 from both sides of the equation: x = 997 - 2 - 667 x = 328 ### 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 70B:
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 579 cm. We can set up an equation: x + x + x = 579. Combining like terms, we get 3x = 579. To find the length of each side, we divide both sides of the equation by 3: x = 579 รท 3 = 193. ### 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?
Llama 3 70B:
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 684m. We can set up the equation: x + x + x = 684. Combine like terms: 3x = 684. Divide both sides by 3: x = 684/3. x = 228. ### Answer: 228m.
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 70B:
Let's call the length of the remaining side "x". Since the perimeter of the triangle is the sum of the lengths of all its sides, we can set up the equation: x + 223 + 46 = 503 Combine the constants on the left-hand side: x + 269 = 503 Subtract 269 from both sides to isolate x: x = 503 - 269 x = 234 ### 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 70B:
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 105m. We can set up the equation: x + x + x = 105. Combine like terms: 3x = 105. Divide both sides by 3: x = 105/3. x = 35. ### 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 70B:
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 306cm. We can set up the equation: x + x + x = 306. Combine like terms: 3x = 306. Divide both sides by 3: x = 306/3. x = 102. ### Answer: 102cm.
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 70B:
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 33 cm. We can set up the equation: x + x + x = 33. Combine like terms: 3x = 33. Divide both sides by 3: x = 33/3. x = 11. ### 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?
Llama 3 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 192 + 159 + x = 861 Combine the known side lengths: 351 + x = 861 Subtract 351 from both sides to isolate x: x = 861 - 351 x = 510 ### 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 70B:
Reasoning: Since the triangle has equal sides, we can divide the perimeter by 3 to find the length of one side. Perimeter = 489 cm Length of one side = Perimeter รท 3 = 489 รท 3 = 163 cm ### Answer: 163 cm
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 70B:
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 696 meters. We can set up the equation: x + x + x = 696. Combine like terms: 3x = 696. Divide both sides by 3: x = 696/3. x = 232. ### 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 70B:
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 Combine the constants on the left side: 759 + x = 804 Subtract 759 from both sides: x = 804 - 759 x = 45 ### Answer: 45m
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 70B:
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 915cm. We can set up the equation: x + x + x = 915. Combine like terms: 3x = 915. Divide both sides by 3: x = 915/3. x = 305. ### 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 70B:
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 564 cm. We can set up the equation: x + x + x = 564. Combining like terms, we get 3x = 564. To find the length of each side, we divide both sides of the equation by 3: x = 564/3 = 188. ### Answer: 188 cm.
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 70B:
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 594 cm. We can set up the equation: x + x + x = 594. Combining like terms, we get 3x = 594. To find the length of each side, we divide both sides of the equation by 3: x = 594 รท 3 = 198. ### Answer: 198 cm.
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 70B:
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 453 cm. We can set up the equation: x + x + x = 453. Combine like terms: 3x = 453. Divide both sides by 3: x = 453/3. x = 151. ### Answer: 151 cm.
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 70B:
Let's call the length of the third side "x". We know that the total perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 250 + 435 + x = 898 Combine the constants on the left-hand side: 685 + x = 898 Subtract 685 from both sides to isolate x: x = 898 - 685 x = 213 ### 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 70B:
Since it's 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 given as 405 cm. So, we can set up the equation: x + x + x = 405 Combine like terms: 3x = 405 Divide both sides by 3: x = 405/3 x = 135 ### 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 70B:
Since it's 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 given as 612 meters. Since all sides are equal, we can set up the equation: x + x + x = 612 Combine like terms: 3x = 612 Divide both sides by 3: x = 612/3 x = 204 So, the length of each side of the equilateral triangle is 204 meters. ### Answer: 204 meters.
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 70B:
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 the lengths of all three sides, so we can set up the equation: x + x + x = 591 Combine like terms: 3x = 591 Divide both sides by 3: x = 591/3 x = 197 So, the length of each side of the triangle 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?
Llama 3 70B:
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 858m. We can set up the equation: x + x + x = 858. Combine like terms: 3x = 858. Divide both sides by 3: x = 858/3. x = 286. ### 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 70B:
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 543 meters. We can set up the equation: x + x + x = 543. Combine like terms: 3x = 543. Divide both sides by 3: x = 543/3. x = 181. ### Answer: 181 meters.
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 70B:
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 its sides, so we can set up the equation: x + x + x = 255 Combine like terms: 3x = 255 Divide both sides by 3: x = 255/3 x = 85 So, the length of each side 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.
Llama 3 70B:
Reasoning: Since it's 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 given as 570mm. We can set up an equation: x + x + x = 570. Combining like terms, we get 3x = 570. To find the length of each side, we divide both sides of the equation by 3: x = 570/3 = 190. ### 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 70B:
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 129m. 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. ### 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 70B:
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 858 meters. We can set up the equation: x + x + x = 858. Combine like terms: 3x = 858. Divide both sides by 3: x = 858/3. x = 286. ### Answer: 286 meters.
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 70B:
Since it's 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 given as 513 km. So, we can set up the equation: x + x + x = 513 Combine like terms: 3x = 513 Divide both sides by 3: x = 513/3 x = 171 ### 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 70B:
Let's call the length of the third side "x" meters. We know that the perimeter of the triangular field is the sum of the lengths of all three sides. So, we can set up the equation: 105 + 434 + x = 828 Now, let's simplify the equation by combining the known sides: 539 + x = 828 Subtract 539 from both sides to isolate x: x = 828 - 539 x = 289 ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of a triangle is the sum of the lengths of all its sides. So, we can set up the equation: 37 + 559 + x = 773 Combine the constants on the left-hand side: 596 + x = 773 Subtract 596 from both sides to isolate x: x = 773 - 596 x = 177 ### Answer: 177 cm
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 70B:
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 714m. We can set up the equation: x + x + x = 714. Combine like terms: 3x = 714. Divide both sides by 3: x = 714/3. x = 238. ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of the garden is the sum of all its sides, so we can set up the equation: 147 + 590 + x = 792 Combine the constants on the left-hand side: 737 + x = 792 Subtract 737 from both sides: x = 792 - 737 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 70B:
Reasoning: Let's call the length of the third side "x". Since the perimeter of a triangle is the sum of all its sides, we can set up the equation: x + 321 + 528 = 871 Combine the constants on the left side: x + 849 = 871 Subtract 849 from both sides: x = 871 - 849 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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 424 + 246 + x = 991 Combine the constants on the left-hand side: 670 + x = 991 Subtract 670 from both sides to isolate x: x = 991 - 670 x = 321 ### 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 70B:
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 936m. We can set up the equation: x + x + x = 936. Combine like terms: 3x = 936. Divide both sides by 3: x = 936/3. x = 312. ### Answer: 312m.
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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 204 + 195 + x = 721 Combine the constants on the left-hand side: 399 + x = 721 Subtract 399 from both sides to isolate x: x = 721 - 399 x = 322 ### Answer: 322m
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
Llama 3 70B:
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 201m. We can set up the equation: x + x + x = 201. Combine like terms: 3x = 201. Divide both sides by 3: x = 201/3. x = 67. ### Answer: 67m.
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 70B:
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 756m. We can set up the equation: x + x + x = 756 Combine like terms: 3x = 756 Divide both sides by 3: x = 756/3 x = 252 So, the length of each side of the equilateral triangle is 252m. ### Answer: 252m
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 70B:
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: 735 + 144 + x = 923 Combine the constants on the left side: 879 + x = 923 Subtract 879 from both sides: x = 923 - 879 x = 44 ### Answer: 44m
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 70B:
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 813 cm. We can set up the equation: x + x + x = 813. Combining like terms, we get 3x = 813. To find the length of each side, we divide both sides of the equation by 3: x = 813 รท 3 = 271. ### 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 70B:
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 834 feet. We can set up the equation: x + x + x = 834. Combine like terms: 3x = 834. Divide both sides by 3: x = 834/3. x = 278. ### Answer: 278 feet.
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 70B:
Reasoning: Since all sides of the triangle are equal in length, we can divide the perimeter by 3 to find the length of one side. Perimeter = 105m Number of sides = 3 Length of one side = Perimeter รท Number of sides = 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 70B:
Reasoning: Since all sides of the triangle are equal, we can divide the perimeter by 3 to find the length of each side. Perimeter = 195cm Number of sides = 3 Length of each side = Perimeter รท Number of sides = 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 70B:
Let's use the fact that the perimeter of a triangle is the sum of the lengths of all its sides. Let the length of the third side be x. We know that the perimeter is 919m, and two of the sides have lengths 350m and 154m. So, we can set up the equation: 350 + 154 + x = 919 Combine the constants on the left-hand side: 504 + x = 919 Subtract 504 from both sides to isolate x: x = 919 - 504 x = 415 ### Answer: 415m
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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 128 + 288 + x = 989 Combine the constants on the left-hand side: 416 + x = 989 Subtract 416 from both sides to isolate x: x = 989 - 416 x = 573 ### 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 70B:
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 321 meters. We can set up an equation: x + x + x = 321. Combining like terms, we get 3x = 321. To find the length of each side, we divide both sides of the equation by 3: x = 321 รท 3 = 107. ### Answer: 107 meters.
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 70B:
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 258 cm. We can set up the equation: x + x + x = 258. Combine like terms: 3x = 258. Divide both sides by 3: x = 258/3. x = 86. ### 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 70B:
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 75m. We can set up the equation: x + x + x = 75. Combine like terms: 3x = 75. Divide both sides by 3: x = 75/3. x = 25. ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of a triangle is the sum of the lengths of all its sides. So, we can set up the equation: 620 + 80 + x = 979 Combine the constants on the left-hand side: 700 + x = 979 Subtract 700 from both sides: x = 979 - 700 x = 279 ### Answer: 279m
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 70B:
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 966 meters. We can set up the equation: x + x + x = 966. Combine like terms: 3x = 966. Divide both sides by 3: x = 966/3. x = 322. ### 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 70B:
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 486 cm. We can set up the equation: x + x + x = 486. Combining like terms, we get 3x = 486. To find the length of each side, we divide both sides of the equation by 3: x = 486 รท 3 = 162. ### 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 70B:
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 948 meters. We can set up the equation: x + x + x = 948. Combine like terms: 3x = 948. Divide both sides by 3: x = 948/3. x = 316. ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 252 + 687 + x = 998 Combine the constants on the left-hand side: 939 + x = 998 Subtract 939 from both sides to isolate x: x = 998 - 939 x = 59 ### 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 70B:
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 given as 618m. We can set up an equation: x + x + x = 618. Combining like terms, we get 3x = 618. To find the length of each side, we divide both sides of the equation by 3: x = 618/3 = 206. ### Answer: 206m
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
Llama 3 70B:
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 the lengths of all three sides, which is 483 meters. We can set up the equation: x + x + x = 483. Combine like terms: 3x = 483. Divide both sides by 3: x = 483/3. x = 161. ### Answer: 161 meters.
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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 262 + 90 + x = 804 Combine the constants on the left-hand side: 352 + x = 804 Subtract 352 from both sides to isolate x: x = 804 - 352 x = 452 ### Answer: 452m
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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 183 + 498 + x = 925 Combine the constants on the left-hand side: 681 + x = 925 Subtract 681 from both sides to isolate x: x = 925 - 681 x = 244 ### Answer: 244m
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 70B:
Let's call the length of the third side "x". We know that the total perimeter of the triangle is 573m, and we are given the lengths of two sides: 103m and 386m. We can set up an equation using the perimeter formula: Perimeter = side1 + side2 + side3 573 = 103 + 386 + x Now, we can simplify the equation by combining the known sides: 573 = 489 + x Subtract 489 from both sides to isolate x: x = 573 - 489 x = 84 ### 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 70B:
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 330m. 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. ### Answer: 110m.
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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 57 + 426 + x = 850 To solve for x, we can subtract 57 and 426 from both sides of the equation: x = 850 - 57 - 426 x = 367 ### 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 70B:
Reasoning: Let's call the length of the third side "x". Since the perimeter of the triangle is the sum of all its sides, we can set up the equation: 265 + 56 + x = 764 Combine the constants on the left side: 321 + x = 764 Subtract 321 from both sides to isolate x: x = 764 - 321 x = 443 ### Answer: 443m
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 70B:
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 723cm. We can set up the equation: x + x + x = 723. Combining like terms, we get 3x = 723. To find the length of each side, we divide both sides of the equation by 3: x = 723 รท 3 = 241. ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 315 + 100 + x = 738 Combine the constants on the left-hand side: 415 + x = 738 Subtract 415 from both sides to isolate x: x = 738 - 415 x = 323 ### 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 70B:
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 762m, and two of the sides have lengths 131m and 147m. Let's call the length of the third side "x". We can set up the equation: 762 = 131 + 147 + x First, let's add the lengths of the two known sides: 131 + 147 = 278 Now, subtract 278 from both sides of the equation: 762 - 278 = x 484 = x ### Answer: 484m
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 70B:
Let's call the length of the third side "x". Since the perimeter of the triangle is 784m, we can set up the equation: x + 472 = 784 To solve for x, we can subtract 472 from both sides of the equation: x = 784 - 472 x = 312 ### Answer: 312m
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 70B:
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 543mm. We can set up the equation: x + x + x = 543. Combine like terms: 3x = 543. Divide both sides by 3: x = 543/3. x = 181. ### 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 70B:
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: 287 + 475 + x = 867 Combine the constants on the left side: 762 + x = 867 Subtract 762 from both sides to isolate x: x = 867 - 762 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 70B:
Reasoning: Let's call the length of the third side "x". Since the perimeter of the triangle is the sum of the lengths of all its sides, we can set up the equation: 828 + 10 + x = 934 Combine the constants on the left side: 838 + x = 934 Subtract 838 from both sides to isolate x: x = 934 - 838 x = 96 ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 109 + 530 + x = 677 Combine the constants on the left-hand side: 639 + x = 677 Subtract 639 from both sides to isolate x: x = 677 - 639 x = 38 ### Answer: 38m
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 70B:
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 582 cm. We can set up the equation: x + x + x = 582. Combining like terms, we get 3x = 582. To find the length of each side, we divide both sides of the equation by 3: x = 582 รท 3 = 194. ### Answer: 194 cm.
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 70B:
Let's call the length of the last side "x". We know that the perimeter of the triangle is the sum of the lengths of all its sides, so we can set up the equation: 259 + 11 + x = 499 Subtract 259 and 11 from both sides of the equation to get: x = 499 - 259 - 11 x = 229 ### 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 70B:
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 966m. We can set up the equation: x + x + x = 966. Combine like terms: 3x = 966. Divide both sides by 3: x = 966/3. x = 322. ### Answer: 322m.
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 70B:
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 894 inches. We can set up the equation: x + x + x = 894. Combine like terms: 3x = 894. Divide both sides by 3: x = 894/3. x = 298. ### Answer: 298 inches.
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 70B:
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 891cm. We can set up the equation: x + x + x = 891. Combine like terms: 3x = 891. Divide both sides by 3: x = 891/3. x = 297. ### 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 70B:
Let's call the length of the third side "x" meters. We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 122 + 245 + x = 762 Combine the known sides: 367 + x = 762 Subtract 367 from both sides: x = 762 - 367 x = 395 ### 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 70B:
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 411m. We can set up the equation: x + x + x = 411. Combine like terms: 3x = 411. Divide both sides by 3: x = 411/3. x = 137. ### Answer: 137m.
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 70B:
Reasoning: Since the triangle has three identical sides, we can divide the total length of the sides by 3 to find the length of each side. Let's divide 72m by 3: 72m รท 3 = 24m ### 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 70B:
Let's call the length of the third side "x". Since the perimeter of the triangle is the sum of the lengths of all its sides, we can set up the equation: 537 + 68 + x = 930 Combine the constants on the left-hand side: 605 + x = 930 Subtract 605 from both sides to isolate x: x = 930 - 605 x = 325 ### 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 70B:
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 657 meters. We can set up the equation: x + x + x = 657. Combine like terms: 3x = 657. Divide both sides by 3: x = 657/3. x = 219. ### Answer: 219 meters.
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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of all its sides, so we can set up the equation: 368 + 230 + x = 909 Combine the constants on the left side: 598 + x = 909 Subtract 598 from both sides to isolate x: x = 909 - 598 x = 311 ### 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 70B:
Reasoning: Let's call the length of the third side "x". Since the perimeter of the triangle is the sum of all its sides, we can set up the equation: 140 + 525 + x = 700 Combine the constants on the left side: 665 + x = 700 Subtract 665 from both sides: x = 700 - 665 x = 35 ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can set up the equation: 484 + 130 + x = 915 Combine the constants on the left-hand side: 614 + x = 915 Subtract 614 from both sides to isolate x: x = 915 - 614 x = 301 ### 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 70B:
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 120 cm. We can set up the equation: x + x + x = 120. Combine like terms: 3x = 120. Divide both sides by 3: x = 120/3. x = 40. ### 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 70B:
Reasoning: Let's call the length of the third side "x". Since the perimeter of the triangular field is the sum of all its sides, we can set up the equation: x + 382 + 151 = 661 Combine the known sides: x + 533 = 661 Subtract 533 from both sides: x = 661 - 533 x = 128 ### Answer: 128m
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 70B:
Let's call the length of the third side "x". Since the perimeter of the triangle is the sum of all its sides, we can set up the equation: 419 + 164 + x = 678 Combine the constants on the left-hand side: 583 + x = 678 Subtract 583 from both sides to isolate x: x = 678 - 583 x = 95 ### Answer: 95 feet
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 70B:
Reasoning: Let's call the length of the remaining side "x". The perimeter of a triangle is the sum of the lengths of all its sides. So, we can set up the equation: x + 186 + 37 = 248 Combine the constants on the left-hand side: x + 223 = 248 Subtract 223 from both sides: x = 248 - 223 x = 25 ### Answer: 25m
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 70B:
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 246 cm. We can set up the equation: x + x + x = 246. Combining like terms, we get 3x = 246. To find the length of each side, we divide both sides of the equation by 3: x = 246 รท 3 = 82. ### Answer: 82 cm.
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 70B:
Let's call the length of the third side "x". We know that the perimeter of a triangle is the sum of the lengths of all its sides. So, we can set up the equation: 180 + 338 + x = 739 Combine the constants on the left-hand side: 518 + x = 739 Subtract 518 from both sides: x = 739 - 518 x = 221 ### 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 70B:
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 684cm. We can set up the equation: x + x + x = 684. Combining like terms, we get 3x = 684. To find the length of each side, we divide both sides of the equation by 3: x = 684 รท 3 = 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 70B:
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 537m. We can set up the equation: x + x + x = 537. Combine like terms: 3x = 537. Divide both sides by 3: x = 537/3. x = 179. ### Answer: 179m.
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 70B:
Reasoning: Let's call the length of the third side "x". Since the perimeter of the triangle is the sum of the lengths of all its sides, we can set up the equation: 110 + 205 + x = 568 Combine the constants on the left-hand side: 315 + x = 568 Subtract 315 from both sides to isolate x: x = 568 - 315 x = 253 ### 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 70B:
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 942mm. We can set up the equation: x + x + x = 942. Combine like terms: 3x = 942. Divide both sides by 3: x = 942/3. x = 314. ### 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 70B:
Let's call the length of the third side "x". Since the perimeter of the triangle is the sum of all its sides, we can set up the equation: 325 + 15 + x = 633 Subtract 325 and 15 from both sides of the equation to isolate x: x = 633 - 325 - 15 x = 633 - 340 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 70B:
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 504 meters. We can set up the equation: x + x + x = 504. Combine like terms: 3x = 504. Divide both sides by 3: x = 504/3. x = 168. ### 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 70B:
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 51 cm. We can set up the equation: x + x + x = 51. Combine like terms: 3x = 51. Divide both sides by 3: x = 51/3. x = 17. ### 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 70B:
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 501 feet. We can set up the equation: x + x + x = 501. Combine like terms: 3x = 501. Divide both sides by 3: x = 501/3. x = 167.33 (but since we can't have a fraction of a foot, we'll round to the nearest whole number). ### 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 70B:
Reasoning: Since the perimeter of an equilateral triangle is the sum of all its sides, and all sides are equal, we can set up the equation: Perimeter = 3 ร side length 411 = 3 ร side length To find the side length, we can divide both sides of the equation by 3: side length = 411 รท 3 side length = 137 ### Answer: 137 meters
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 70B:
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 114cm. We can set up the equation: x + x + x = 114. Combine like terms: 3x = 114. Divide both sides by 3: x = 114/3. x = 38. ### 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 70B:
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 69m. 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. ### 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 70B:
Let's call the length of the third side "x". We know that the perimeter of a triangle is the sum of the lengths of all its sides. So, we can set up the equation: 464 + 377 + x = 907 Combine the constants on the left-hand side: 841 + x = 907 Subtract 841 from both sides: x = 907 - 841 x = 66 ### 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 70B:
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 966m. We can set up the equation: x + x + x = 966. Combine like terms: 3x = 966. Divide both sides by 3: x = 966/3. x = 322. ### Answer: 322m.
Expected answer: 322
Correct? Yes