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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 990cm. x = 990cm / 3 = <<990/3=330>>330cm. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 2 + 667 + x = 997 Solving for x, we get x = 997 - 2 - 667 = <<997-2-667=328>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side of the equilateral triangle. Then, 3x = 579 cm. Solving for x, we get x = 579/3 = <<579/3=193>>193 cm. ### Answer: 193 cm
Expected answer: 193
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 684. x = 684/3 = <<684/3=228>>228m. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all three sides. Let x be the length of the remaining side. Then, 223 + 46 + x = 503 Solving for x, we get x = 503 - 223 - 46 = <<503-223-46=234>>234 meters. ### Answer: 234 meters
Expected answer: 234
Correct? Yes
Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 105m. Solving for x, we get x = 105m/3 = <<105/3=35>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 306cm. Solving for x, we get x = 306cm/3 = <<306/3=102>>102cm. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x cm. Then, 3x = 33 cm. Solving for x, we get x = 33/3 = <<33/3=11>>11 cm. ### Answer: 11 cm
Expected answer: 11
Correct? Yes
Problem: A triangle has a perimeter of 861m. Two of the sides are known to be 192m and 159m in length. Can you find the length of the third side?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's call the length of the third side x. So, 192 + 159 + x = 861 Combining the known side lengths, we get: 351 + x = 861 Subtracting 351 from both sides, we get: x = 861 - 351 x = 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?
Mixtral 8x22B:
Reasoning: Since the triangle has equal sides, it is an equilateral triangle. The perimeter of an equilateral triangle is three times the length of one side. Therefore, the length of one side is 489/3 = <<489/3=163>>163 centimeters. ### Answer: 163 centimeters
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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x meters. Then, 3x = 696 meters. Solving for x, we get x = 696/3 = <<696/3=232>>232 meters. ### Answer: 232 meters
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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all three sides. Let x be the length of the third side. Then, 180 + 579 + x = 804 Solving for x, we get x = 804 - 180 - 579 = <<804-180-579=45>>45m ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x cm. Then, 3x = 915 cm. Solving for x, we get x = 915/3 = <<915/3=305>>305 cm. ### Answer: 305 cm
Expected answer: 305
Correct? Yes
Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x cm. Then, 3x = 564 cm. Solving for x, we get x = 564/3 = <<564/3=188>>188 cm. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x cm. Then, the perimeter is 3x cm. Since the perimeter is 594 cm, we have 3x = 594. Solving for x, we get x = 594/3 = <<594/3=198>>198 cm. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of the triangle is the sum of the lengths of all three sides. Since the triangle is equilateral, each side is equal to the perimeter divided by 3. 453 cm / 3 = <<453/3=151>>151 cm ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 250 + 435 + x = 898 Solving for x, we get x = 898 - 250 - 435 = <<898-250-435=213>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x cm. Then, 3x = 405 cm. Solving for x, we get x = 405/3 = <<405/3=135>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. To find the length of each side, we can divide the total perimeter by 3. 612 meters / 3 = <<612/3=204>>204 meters So, each side of the equilateral triangle is 204 meters long. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x cm. Then, 3x = 591 cm. Solving for x, we get x = 591/3 = <<591/3=197>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 858. Solving for x, we get x = 858/3 = <<858/3=286>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Therefore, the length of each side is the perimeter divided by 3. The length of each side is 543/3 = <<543/3=181>>181 meters. ### 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?
Mixtral 8x22B:
Reasoning: Since the triangle has three equal sides, it is an equilateral triangle. The perimeter of an equilateral triangle is three times the length of one side. Therefore, the length of each side is the perimeter divided by 3. Length of each side = 255/3 = <<255/3=85>>85 meters. ### Answer: 85 meters
Expected answer: 85
Correct? Yes
Problem: An equilateral triangle has a perimeter of 570mm. Find the length of each side of this triangle.
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x mm. Then, 3x = 570 mm. Solving for x, we get x = 570/3 = <<570/3=190>>190 mm. ### Answer: 190 mm
Expected answer: 190
Correct? Yes
Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 129m. Solving for x, we get x = 129m/3 = <<129/3=43>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 858. Solving for x, we get x = 858/3 = <<858/3=286>>286 meters. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. Therefore, to find the length of each side, we can divide the perimeter by 3. 513 km / 3 = <<513/3=171>>171 km 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's call the length of the third side x. The perimeter of the field is 828 meters, so we have: 105 + 434 + x = 828 Now, we can solve for x: x = 828 - 105 - 434 x = 289 So, the third side of the field is 289 meters long. ### Answer: 289 meters
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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let the length of the third side be x cm. Then, 37 + 559 + x = 773 Solving for x, we get x = 773 - 37 - 559 = <<773-37-559=177>>177 cm. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x meters. Then, 3x = 714. Solving for x, we get x = 714/3 = <<714/3=238>>238 meters. ### Answer: 238 meters
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?
Mixtral 8x22B:
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. The perimeter of the garden is given as 792m, so we have: 147m + 590m + x = 792m Now, we can solve for x: x = 792m - 147m - 590m x = 55m So, the length of the third side is 55m. ### Answer: 55m
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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 321 + 528 + x = 871 Solving for x, we get x = 871 - 321 - 528 = <<871-321-528=22>>22 meters. ### Answer: 22 meters
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.
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's call the length of the third side x. So, 424 + 246 + x = 991 Combining the known side lengths, we get: 670 + x = 991 Subtracting 670 from both sides, we get: x = 991 - 670 x = 321 Therefore, 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of the triangle is the sum of the lengths of all three sides. Since the triangle is equilateral, each side is equal to the perimeter divided by 3. So, each side of the triangle is 936m/3 = <<936/3=312>>312m long. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 204 + 195 + x = 721 Solving for x, we get x = 721 - 204 - 195 = <<721-204-195=322>>322m ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x meters. Then, 3x = 201. Solving for x, we get x = 201/3 = <<201/3=67>>67 meters. ### Answer: 67 meters
Expected answer: 67
Correct? Yes
Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x meters. Then, the perimeter is 3x meters. Since the perimeter is 756 meters, we have 3x = 756. Solving for x, we get x = 756/3 = <<756/3=252>>252 meters. ### Answer: 252 meters
Expected answer: 252
Correct? Yes
Problem: The perimeter of a triangle is 923m. Two of its sides are 735m and 144m long respectively. What is the length of the third side?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let the length of the third side be x meters. Then, 735 + 144 + x = 923 x = 923 - 735 - 144 x = 54 ### Answer: 54m
Expected answer: 44
Correct? No
Problem: An equilateral triangle has a perimeter of 813 cm. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x cm. Then, 3x = 813 cm. Solving for x, we get x = 813/3 = <<813/3=271>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 834 feet. Solving for x, we get x = 834/3 = <<834/3=278>>278 feet. ### 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?
Mixtral 8x22B:
Reasoning: Since all sides of the triangle are equal in length, we can find the length of one side by dividing the perimeter by 3. 105m / 3 = <<105/3=35>>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?
Mixtral 8x22B:
Reasoning: Since all sides of the triangle are equal, it is an equilateral triangle. The perimeter of an equilateral triangle is the sum of its three equal sides. Therefore, each side of the triangle is 195cm/3 = <<195/3=65>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 350 + 154 + x = 919 Solving for x, we get x = 919 - 350 - 154 = <<919-350-154=415>>415m ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 128 + 288 + x = 989 Solving for x, we get x = 989 - 128 - 288 = <<989-128-288=573>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of the triangle is the sum of the lengths of all three sides. Since all sides are equal, the length of each side is the perimeter divided by 3. The length of each side is 321/3 = <<321/3=107>>107 meters. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x cm. Then, 3x = 258 cm. Solving for x, we get x = 258/3 = <<258/3=86>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of the triangle is the sum of the lengths of all three sides. Since the perimeter is 75m, each side of the triangle is 75m/3 = <<75/3=25>>25m long. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let the length of the third side be x meters. Then, 620 + 80 + x = 979 Solving for x, we get x = 979 - 620 - 80 = <<979-620-80=279>>279 meters. ### Answer: 279 meters
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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x meters. Then, the perimeter is 3x meters. Since the perimeter is 966 meters, we have 3x = 966. Solving for x, we get x = 966/3 = <<966/3=322>>322 meters. ### Answer: 322 meters
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 486 cm. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x cm. Then, 3x = 486 cm. Solving for x, we get x = 486/3 = <<486/3=162>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 948. Solving for x, we get x = 948/3 = <<948/3=316>>316 meters. ### Answer: 316 meters
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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The third side can be found by subtracting the lengths of the first two sides from the total perimeter. The third side is 998m - 252m - 687m = <<998-252-687=59>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side of the equilateral triangle. Then, 3x = 618m. Solving for x, we get x = 618m/3 = <<618/3=206>>206m. ### Answer: 206m
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 483. Solving for x, we get x = 483/3 = <<483/3=161>>161 meters. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's call the length of the third side x. We know that the perimeter is 804m, and we have the lengths of two sides: 262m and 90m. So, we can write the equation: 262 + 90 + x = 804 Solving for x, we get: x = 804 - 262 - 90 = <<804-262-90=452>>452m ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 183 + 498 + x = 925 Solving for x, we get x = 925 - 183 - 498 = <<925-183-498=244>>244m. ### 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?
Mixtral 8x22B:
Reasoning: The sum of the lengths of the two known sides is 103m + 386m = <<103+386=489>>489m. The length of the third side is the total perimeter minus the sum of the lengths of the two known sides, which is 573m - 489m = <<573-489=84>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 330m. Solving for x, we get x = 330m/3 = <<330/3=110>>110m. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's call the length of the third side x. So, 57m + 426m + x = 850m Solving for x, we get x = 850m - 57m - 426m = <<850-57-426=367>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 265m + 56m + x = 764m Solving for x, we get x = 764m - 265m - 56m = <<764-265-56=443>>443m ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 723cm. x = 723cm / 3 = <<723/3=241>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all three sides. Let x be the length of the third side. The perimeter of the triangle is 315m + 100m + x = 738m. Solving for x, we get x = 738m - 315m - 100m = <<738-315-100=323>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all three sides. Let x be the length of the third side. The perimeter is given as 762m, so we have: 131m + 147m + x = 762m Solving for x, we get: x = 762m - 131m - 147m = <<762-131-147=484>>484m ### 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?
Mixtral 8x22B:
Reasoning: Let the length of the third side be x meters. The sum of the lengths of the other two sides is 472m. The perimeter of the triangle is the sum of the lengths of all three sides, which is 784m. So, x + 472 = 784. Solving for x, we get x = 784 - 472 = <<784-472=312>>312m. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. So, the length of each side is the perimeter divided by 3. The length of each side is 543mm/3 = <<543/3=181>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all three sides. Let x be the length of the third side. The perimeter is given as 867m, so we have: 287m + 475m + x = 867m Solving for x, we get: x = 867m - 287m - 475m = <<867-287-475=105>>105m ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all its sides. Let the length of the third side be x meters. Then, 828 + 10 + x = 934 x = 934 - 838 x = <<934-838=96>>96 meters. ### Answer: 96 meters
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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 109 + 530 + x = 677 Solving for x, we get x = 677 - 109 - 530 = <<677-109-530=38>>38m. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x cm. Then, 3x = 582 cm. Solving for x, we get x = 582/3 = <<582/3=194>>194 cm. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all its sides. Let's call the length of the last side x. The perimeter is given as 499m, so we have: 259m + 11m + x = 499m Now, we can solve for x: x = 499m - 259m - 11m x = 229m So, the length of the last side is 229m. ### Answer: 229m
Expected answer: 229
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 966. Solving for x, we get x = 966/3 = <<966/3=322>>322m. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let x be the length of each side of the triangle. Then, 3x = 894. Solving for x, we get x = 894/3 = <<894/3=298>>298 inches. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 891cm. x = 891cm / 3 = <<891/3=297>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's denote the length of the third side as x. The equation for the perimeter of the triangle is: 122 + 245 + x = 762 Solving for x: x = 762 - 122 - 245 x = 395 Therefore, the length of the third side is 395 meters. ### Answer: 395 meters
Expected answer: 395
Correct? Yes
Problem: An equilateral triangle has a perimeter of 411m. What is the length of each side of the triangle?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x meters. Then, 3x = 411. Solving for x, we get x = 411/3 = <<411/3=137>>137 meters. ### Answer: 137 meters
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?
Mixtral 8x22B:
Reasoning: Since the triangle has three identical sides, it is an equilateral triangle. The total length of the sides is 72m, so each side is 72m/3 = <<72m/3=24m>>24m long. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 537 + 68 + x = 930 Solving for x, we get x = 930 - 537 - 68 = <<930-537-68=325>>325 meters. ### Answer: 325 meters
Expected answer: 325
Correct? Yes
Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 657. Solving for x, we get x = 657/3 = <<657/3=219>>219 meters. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. The perimeter of the triangle is 368m + 230m + x = 909m. Solving for x, we get x = 909m - 368m - 230m = <<909-368-230=311>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's call the length of the third side x. The perimeter is given as 700m, so we have: 140m + 525m + x = 700m Solving for x, we get: x = 700m - 140m - 525m x = 35m So the length of the third side is 35m. ### Answer: 35m
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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 484 + 130 + x = 915 Solving for x, we get x = 915 - 484 - 130 = <<915-484-130=301>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of the triangle is the sum of the lengths of all three sides. Since the perimeter is 120 cm, each side of the triangle is 120/3 = <<120/3=40>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let the length of the third side be x. Then, 382 + 151 + x = 661 Solving for x, we get x = 661 - 382 - 151 = <<661-382-151=128>>128m. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 419 + 164 + x = 678 Solving for x, we get x = 678 - 419 - 164 = <<678-419-164=95>>95 feet. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the remaining side. Then, 186 + 37 + x = 248. Solving for x, we get x = 248 - 186 - 37 = <<248-186-37=25>>25m. ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 246 centimeters. Solving for x, we get x = 246/3 = <<246/3=82>>82 centimeters. ### Answer: 82 centimeters
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.
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let's denote the length of the third side as x. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have: 180 + 338 > x Also, the sum of the lengths of the three sides must equal the perimeter: 180 + 338 + x = 739 Now, we can solve for x: x = 739 - (180 + 338) x = 739 - 518 x = 221 Therefore, the length of the third side is 221 meters. ### Answer: 221 meters
Expected answer: 221
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x cm. Then, 3x = 684 cm. Solving for x, we get x = 684/3 = <<684/3=228>>228 cm. ### Answer: 228 cm
Expected answer: 228
Correct? Yes
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x. Then, 3x = 537. Solving for x, we get x = 537/3 = <<537/3=179>>179m. ### 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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let x be the length of the third side. Then, 110 + 205 + x = 568 Solving for x, we get x = 568 - 110 - 205 = <<568-110-205=253>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side. Then, 3x = 942mm. Solving for x, we get x = 942mm / 3 = <<942/3=314>>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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of all three sides. Let x be the length of the third side. The perimeter is 325 + 15 + x = 633 Solving for x, we get x = 633 - 325 - 15 = <<633-325-15=293>>293 meters. ### Answer: 293 meters
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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of the triangle is the sum of the lengths of its sides. Since the perimeter is 504 meters, each side of the triangle is 504/3 = <<504/3=168>>168 meters long. ### Answer: 168 meters
Expected answer: 168
Correct? Yes
Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three equal sides. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x cm. Then, 3x = 51 cm. Solving for x, we get x = 51/3 = <<51/3=17>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let x be the length of each side of the triangle. Then, 3x = 501 feet. Solving for x, we get x = 501/3 = <<501/3=167>>167 feet. ### Answer: 167 feet
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?
Mixtral 8x22B:
Reasoning: The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Since all sides of an equilateral triangle are equal in length, we can find the length of one side by dividing the perimeter by 3. 411/3 = <<411/3=137>>137 meters ### 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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let the length of each side be x. Then, 3x = 114cm. Solving for x, we get x = 114/3 = <<114/3=38>>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?
Mixtral 8x22B:
Reasoning: An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Let the length of each side be x meters. Then, 3x = 69 x = 69/3 = <<69/3=23>>23 So, the length of each side of the equilateral triangle is 23 meters. ### Answer: 23 meters
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?
Mixtral 8x22B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Let the length of the third side be x meters. Then, 464 + 377 + x = 907 Solving for x, we get x = 907 - 464 - 377 = <<907-464-377=66>>66 meters. ### Answer: 66 meters
Expected answer: 66
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Mixtral 8x22B:
Reasoning: An equilateral triangle has three sides of equal length. The perimeter of an equilateral triangle is the sum of its three sides. Let x be the length of each side of the equilateral triangle. Then, 3x = 966m. Solving for x, we get x = 966m/3 = <<966/3=322>>322m. ### Answer: 322m
Expected answer: 322
Correct? Yes