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?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 990/3 = <<990/3=330>>330cm. ### Answer: 330
Expected answer: 330
Correct? Yes
Problem: A triangle has a perimeter of 997m. Two of its sides have lengths of 2m and 667m. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 997-2-667 = <<997-2-667=328>>328m. ### Answer: 328
Expected answer: 328
Correct? Yes
Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 579/3 = <<579/3=193>>193 cm. ### Answer: 193
Expected answer: 193
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 684/3 = <<684/3=228>>228m. ### Answer: 228
Expected answer: 228
Correct? Yes
Problem: A triangle has a perimeter of 503 meters. One side of the triangle is 223 meters long and another side is 46 meters long. What is the length of the remaining side?
InternLM-Math Base 20B:
Reasoning: The length of the remaining side is 503-223-46 = <<503-223-46=234>>234 meters. ### Answer: 234
Expected answer: 234
Correct? Yes
Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 105/3 = <<105/3=35>>35m. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: An equilateral triangle has a perimeter of 306cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one side of the triangle is 306/3 = <<306/3=102>>102cm. ### Answer: 102
Expected answer: 102
Correct? Yes
Problem: An equilateral triangle has a perimeter of 33 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 33/3 = <<33/3=11>>11 cm. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: A triangle has a perimeter of 861m. Two of the sides are known to be 192m and 159m in length. Can you find the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 861-192-159 = <<861-192-159=410>>410m. ### Answer: 410
Expected answer: 510
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. If each side is of equal length, then the perimeter is three times the length of one side. So, 489 = 3x. Dividing both sides by 3, we get x = <<489/3=163>>163. So, the length of one side is 163 centimeters. ### Answer: 163
Expected answer: 163
Correct? Yes
Problem: An equilateral triangle has a perimeter of 696 meters. What is the length of each side of this triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 696/3 = <<696/3=232>>232 meters is the length of one side of the triangle. ### 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?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 804-180-579 = <<804-180-579=45>>45m. ### Answer: 45
Expected answer: 45
Correct? Yes
Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one of the sides of the triangle is 915/3 = <<915/3=305>>305cm. ### Answer: 305
Expected answer: 305
Correct? Yes
Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 564/3 = <<564/3=188>>188 cm. ### Answer: 188
Expected answer: 188
Correct? Yes
Problem: An equilateral triangle has a perimeter of 594 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 594/3 = <<594/3=198>>198 cm. ### Answer: 198
Expected answer: 198
Correct? Yes
Problem: An equilateral triangle has a perimeter of 453 cm. How long is each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one side of the triangle is 453/3 = <<453/3=151>>151 cm. ### Answer: 151
Expected answer: 151
Correct? Yes
Problem: A triangle has a total perimeter of 898m. The lengths of two of its sides are 250m and 435m respectively. Can you find the length of the third side of the triangle?
InternLM-Math Base 20B:
Reasoning: The length of the third side of the triangle is 898-250-435 = <<898-250-435=113>>113m. ### Answer: 113
Expected answer: 213
Correct? No
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Therefore, the length of one side of the triangle is 405/3 = <<405/3=135>>135 cm. ### Answer: 135
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?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. So, the length of one side of the triangle is 612/3 = <<612/3=204>>204 meters. ### Answer: 204
Expected answer: 204
Correct? Yes
Problem: An equilateral triangle has a perimeter of 591 cm. Can you find the length of each side of this triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one side of the triangle is 591/3 = <<591/3=197>>197 cm. ### Answer: 197
Expected answer: 197
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 858/3 = <<858/3=286>>286m. ### Answer: 286
Expected answer: 286
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543 meters. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 543/3 = <<543/3=181>>181 meters. ### Answer: 181
Expected answer: 181
Correct? Yes
Problem: A triangle has three equal sides. If the perimeter of the triangle is 255 meters, what is the length of each side?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Since the triangle has three equal sides, the perimeter is 3 times the length of one side. So, the length of one side is 255/3 = <<255/3=85>>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.
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one side of the triangle is 570/3 = <<570/3=190>>190mm. ### Answer: 190
Expected answer: 190
Correct? Yes
Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 129/3 = <<129/3=43>>43 m. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858 meters. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 858/3 = <<858/3=286>>286 meters. ### Answer: 286
Expected answer: 286
Correct? Yes
Problem: A triangle has a perimeter of 513 km, and it's known to be an equilateral triangle - meaning all three sides are of equal length. Can you determine how long each side of this triangle is?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Since the triangle is equilateral, all three sides are of equal length. Let's call this length x. Then, the perimeter of the triangle is 3x. We know that the perimeter of the triangle is 513 km, so we can write the equation 3x = 513. Solving for x, we get x = 171. Therefore, each side of the triangle is 171 km long. ### Answer: 171
Expected answer: 171
Correct? Yes
Problem: A triangular field has a perimeter of 828 meters. Two sides of the field are 105 and 434 meters long. How long is the third side of the field?
InternLM-Math Base 20B:
Reasoning: The third side of the field is 828-105-434 = <<828-105-434=289>>289 meters long. ### Answer: 289
Expected answer: 289
Correct? Yes
Problem: The perimeter of a triangle is 773 cm. Two of its sides measure 37 cm and 559 cm, respectively. Find the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 773-37-559 = <<773-37-559=187>>187 cm. ### Answer: 187
Expected answer: 177
Correct? No
Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 714/3 = <<714/3=238>>238 ### Answer: 238
Expected answer: 238
Correct? Yes
Problem: In a large triangular garden, one of its sides is 147m and another side is 590m. If the perimeter of the garden is 792m, can you find the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 792-147-590 = <<792-147-590=205>>205m. ### Answer: 205
Expected answer: 55
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 871-321-528 = <<871-321-528=120>>120 meters. ### Answer: 120
Expected answer: 22
Correct? No
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.
InternLM-Math Base 20B:
Reasoning: The length of the third side of the triangle is 991-424-246 = <<991-424-246=321>>321m. ### Answer: 321
Expected answer: 321
Correct? Yes
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 936/3 = <<936/3=312>>312m is the length of one side of the triangle. ### Answer: 312
Expected answer: 312
Correct? Yes
Problem: A triangle has a perimeter of 721m. Two of its sides have lengths of 204m and 195m, respectively. What is the length of the third side of the triangle?
InternLM-Math Base 20B:
Reasoning: The length of the third side of the triangle is 721-204-195 = <<721-204-195=422>>422m. ### Answer: 422
Expected answer: 322
Correct? No
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 201/3 = <<201/3=67>>67 m. ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one of the sides of the triangle is 756/3 = <<756/3=252>>252m. ### Answer: 252
Expected answer: 252
Correct? Yes
Problem: The perimeter of a triangle is 923m. Two of its sides are 735m and 144m long respectively. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 923-735-144 = <<923-735-144=144>>144m. ### Answer: 144
Expected answer: 44
Correct? No
Problem: An equilateral triangle has a perimeter of 813 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 813/3 = <<813/3=271>>271 cm. ### Answer: 271
Expected answer: 271
Correct? Yes
Problem: An equilateral triangle has a perimeter of 834 feet. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 834/3 = <<834/3=278>>278 feet. ### Answer: 278
Expected answer: 278
Correct? Yes
Problem: A triangle has a perimeter of 105m and all its sides are equal in length. How long is one side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Since all the sides of the triangle are equal, the length of one side is 105/3 = <<105/3=35>>35m. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: A triangle has a perimeter of 195cm. Given that all sides of the triangle are equal, what is the length of each side?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Since all sides of the triangle are equal, the length of each side is 195/3 = <<195/3=65>>65cm. ### Answer: 65
Expected answer: 65
Correct? Yes
Problem: A triangle has a perimeter of 919m. You know that one of its sides is 350m long and the other side is 154m long. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 919-350-154 = <<919-350-154=315>>315m. ### Answer: 315
Expected answer: 415
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The third side is 989-128-288 = <<989-128-288=343>>343m long. ### Answer: 343
Expected answer: 573
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Since the triangle is equilateral, all sides are equal. Therefore, the length of each side is 321/3 = <<321/3=107>>107 meters. ### Answer: 107
Expected answer: 107
Correct? Yes
Problem: An equilateral triangle has a perimeter of 258 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 258/3 = <<258/3=86>>86 cm. ### Answer: 86
Expected answer: 86
Correct? Yes
Problem: An equilateral triangle has a perimeter of 75m. What is the length of each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of the triangle is 75m. Since the triangle is equilateral, each side of the triangle is 75/3 = <<75/3=25>>25m. ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: The perimeter of a triangle is 979m. Two of its sides are 620m and 80m respectively. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 979-620-80 = <<979-620-80=239>>239m. ### Answer: 239
Expected answer: 279
Correct? No
Problem: An equilateral triangle has a perimeter of 966 meters. What is the length of each side of this triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one side of the triangle is 966/3 = <<966/3=322>>322 meters. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 486 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 486/3 = <<486/3=162>>162 cm. ### Answer: 162
Expected answer: 162
Correct? Yes
Problem: An equilateral triangle has a perimeter of 948 meters. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 948/3 = <<948/3=316>>316 meters. ### Answer: 316
Expected answer: 316
Correct? Yes
Problem: A scalene triangle has three sides of different lengths. The first side is 252m, and the second side is 687m. The total perimeter of the triangle is 998m. Can you find the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 998-252-687 = <<998-252-687=109>>109m. ### Answer: 109
Expected answer: 59
Correct? No
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 618/3 = <<618/3=206>>206m. ### Answer: 206
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 483/3 = <<483/3=161>>161 meters. ### Answer: 161
Expected answer: 161
Correct? Yes
Problem: A triangle has a perimeter of 804m. One of its sides is 262m long and another is 90m long. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 804-262-90 = <<804-262-90=352>>352m. ### Answer: 352
Expected answer: 452
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The third side is 925-183-498 = <<925-183-498=244>>244m. ### Answer: 244
Expected answer: 244
Correct? Yes
Problem: A scalene triangle has a total perimeter of 573m. One of its sides measures 103m and another side measures 386m. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The third side of the triangle measures 573-103-386 = <<573-103-386=184>>184m. ### Answer: 184
Expected answer: 84
Correct? No
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 330/3 = <<330/3=110>>110m. ### Answer: 110
Expected answer: 110
Correct? Yes
Problem: A triangle has a perimeter of 850m. Two of its sides have lengths of 57m and 426m, respectively. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The third side has a length of 850-57-426 = <<850-57-426=267>>267m. ### Answer: 267
Expected answer: 367
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The third side is 764-265-56 = <<764-265-56=243>>243m in length. ### Answer: 243
Expected answer: 443
Correct? No
Problem: An equilateral triangle has a perimeter of 723cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 723/3 = <<723/3=241>>241 ### Answer: 241
Expected answer: 241
Correct? Yes
Problem: A triangle has a side with a length of 315m and another side with a length of 100m. If the perimeter of the triangle is 738m, what is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Let x be the length of the third side. Then, 315+100+x = 738. Subtracting 315 and 100 from both sides, we get x = 738-315-100 = <<738-315-100=313>>313. Therefore, the length of the third side is 313m. ### Answer: 313
Expected answer: 323
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 762-131-147 = <<762-131-147=484>>484m. ### Answer: 484
Expected answer: 484
Correct? Yes
Problem: A triangle has a perimeter of 784m and you know the sum of two of its sides is 472m. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 784-472 = <<784-472=312>>312m. ### Answer: 312
Expected answer: 312
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543mm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 543/3 = <<543/3=181>>181 mm. ### Answer: 181
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?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 867-287-475 = <<867-287-475=305>>305m. ### Answer: 305
Expected answer: 105
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 934-828-10 = <<934-828-10=96>>96m. ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: A triangle has a perimeter of 677m. Two of its sides measure 109m and 530m respectively. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The third side of the triangle is 677-109-530 = <<677-109-530=48>>48m. ### Answer: 48
Expected answer: 38
Correct? No
Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 582/3 = <<582/3=194>>194 cm. ### Answer: 194
Expected answer: 194
Correct? Yes
Problem: A triangle has a perimeter of 499m. Its largest side is 259m long, and one of the other sides is 11m long. What is the length of the last side?
InternLM-Math Base 20B:
Reasoning: The last side is 499-259-11 = <<499-259-11=129>>129m long. ### Answer: 129
Expected answer: 229
Correct? No
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 966/3 = <<966/3=322>>322m. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 894 inches. What is the length of each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of the triangle is 894 inches. Since the triangle is equilateral, each side of the triangle is 894/3 = <<894/3=298>>298 inches. ### Answer: 298
Expected answer: 298
Correct? Yes
Problem: An equilateral triangle has a perimeter of 891cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one side of the triangle is 891/3 = <<891/3=297>>297cm. ### Answer: 297
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?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 762-122-245 = <<762-122-245=495>>495 meters. ### Answer: 495
Expected answer: 395
Correct? No
Problem: An equilateral triangle has a perimeter of 411m. What is the length of each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of the triangle is 411m. Since the triangle is equilateral, each side of the triangle is 411/3 = <<411/3=137>>137m. ### Answer: 137
Expected answer: 137
Correct? Yes
Problem: A triangle has three identical sides and the total length of the sides is 72m. What is the length of each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The length of each side of the triangle is 72/3 = <<72/3=24>>24m. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: A large triangle has a perimeter of 930 meters. Two of its sides measure 537 meters and 68 meters respectively. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The third side of the triangle is 930-537-68 = <<930-537-68=345>>345 meters long. ### Answer: 345
Expected answer: 325
Correct? No
Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 657/3 = <<657/3=219>>219 meters. ### Answer: 219
Expected answer: 219
Correct? Yes
Problem: A scalene triangle has a side that measures 368m and another side that measures 230m. If the perimeter of the triangle is 909m, what is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The perimeter of the triangle is 909m. The length of the third side is 909-368-230 = <<909-368-230=241>>241m. ### Answer: 241
Expected answer: 311
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The third side is 700-140-525 = <<700-140-525=135>>135 m long. ### Answer: 135
Expected answer: 35
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The third side of the triangle is 915-484-130 = <<915-484-130=301>>301cm. ### Answer: 301
Expected answer: 301
Correct? Yes
Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 120/3 = <<120/3=40>>40 ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A triangular field has a perimeter of 661m. Two sides of the field are known to be 382m and 151m respectively. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 661-382-151 = <<661-382-151=228>>228m. ### Answer: 228
Expected answer: 128
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The third side of the triangle has a length of 678-419-164 = <<678-419-164=195>>195 feet. ### Answer: 195
Expected answer: 95
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The length of the remaining side is 248-186-37 = <<248-186-37=25>>25m. ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: An equilateral triangle has a perimeter of 246 centimeters. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 246/3 = <<246/3=82>>82 ### Answer: 82
Expected answer: 82
Correct? Yes
Problem: The total perimeter of a triangular field is 739 meters. Two of its sides measure 180 meters and 338 meters respectively. Find the length of the third side.
InternLM-Math Base 20B:
Reasoning: The length of the third side is 739-180-338 = <<739-180-338=221>>221 meters. ### Answer: 221
Expected answer: 221
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one of the sides of the triangle is 684/3 = <<684/3=228>>228cm. ### Answer: 228
Expected answer: 228
Correct? Yes
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one of the sides of the triangle is 537/3 = <<537/3=179>>179m. ### Answer: 179
Expected answer: 179
Correct? Yes
Problem: A triangle has a perimeter of 568m. The lengths of two of its sides are 110m and 205m. What is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 568-110-205 = <<568-110-205=353>>353m. ### Answer: 353
Expected answer: 253
Correct? No
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 942/3 = <<942/3=314>>314 mm. ### Answer: 314
Expected answer: 314
Correct? Yes
Problem: A triangular garden has one side that is 325 meters long and another that is 15 meters long. The total perimeter of the triangle is 633 meters. What is the length of the third side of the garden?
InternLM-Math Base 20B:
Reasoning: The third side of the triangle is 633-325-15 = <<633-325-15=193>>193 meters long. ### Answer: 193
Expected answer: 293
Correct? No
Problem: An equilateral triangle has a perimeter of 504 meters. What is the length of each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 504/3 = <<504/3=168>>168 meters. ### Answer: 168
Expected answer: 168
Correct? Yes
Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side of the triangle is 51/3 = <<51/3=17>>17 cm. ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: An equilateral triangle has a perimeter of 501 feet. What is the length of each side of the triangle?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 501/3 = <<501/3=167>>167 feet is the length of each side of the triangle. ### 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?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 411/3 = <<411/3=137>>137 meters is the length of one side of the triangle. ### Answer: 137
Expected answer: 137
Correct? Yes
Problem: An equilateral triangle has a perimeter of 114cm. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 114/3 = <<114/3=38>>38 cm. ### Answer: 38
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 69/3 = <<69/3=23>>23m. ### Answer: 23
Expected answer: 23
Correct? Yes
Problem: A triangle has sides of lengths 464m and 377m respectively. If the total perimeter of the triangle is 907m, what is the length of the third side?
InternLM-Math Base 20B:
Reasoning: The length of the third side is 907-464-377 = <<907-464-377=76>>76m. ### Answer: 76
Expected answer: 66
Correct? No
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
InternLM-Math Base 20B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of each side is 966/3 = <<966/3=322>>322m. ### Answer: 322
Expected answer: 322
Correct? Yes