LLemma 7B on 3.MD.D.8-triangle
Common Core Standard 3.MD.D.8-triangle
This standard covers the following:
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Problem: An equilateral triangle has a perimeter of 990cm. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 990 x = 990/3 = <<990/3=330>>330 Each of the sides of the triangle is 330cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 997 - (2 + 667) = <<997-(2+667)=120>>120m. ### Answer: 120
Expected answer: 328
Correct? No
Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 579 x = <<579/3=193>>193 cm Each of the sides of the triangle is 193 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 684m 3 times the length of one of its sides = 684/3 = <<684/3=228>>228m The length of each of its sides is 228m. ### Answer: 228
Expected answer: 228
Correct? Yes
Problem: A triangle has a perimeter of 503 meters. One side of the triangle is 223 meters long and another side is 46 meters long. What is the length of the remaining side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 105 x = 105/3 = <<105/3=35>>35 Each of the sides of the triangle is 35m long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 306cm. 3x = 306 x = 306/3 = <<306/3=102>>102cm Each of its sides is 102cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 33 cm. 3x = 33 x = 33/3 = <<33/3=11>>11 Each of the sides of the triangle is 11 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. 489/3 = <<489/3=163>>163 centimeters is the length of one side. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. 3 times the length of one side = 696 meters The length of one side = <<696/3=232>>232 meters ### Answer: 232
Expected answer: 232
Correct? Yes
Problem: The perimeter of a triangle is 804m. One side of the triangle is 180m long, and another side is 579m long. What is the length of the third side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. The length of the third side is 804 - 180 - 579 = <<804-180-579=145>>145m. ### Answer: 145
Expected answer: 45
Correct? No
Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 915 x = 915/3 = <<915/3=305>>305 Each of the sides of the triangle is 305cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 564 x = 564/3 = <<564/3=188>>188 cm Each of the sides of the triangle is 188 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 594 x = 594/3 = <<594/3=198>>198 cm Each of the sides of the triangle is 198 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. Each 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side of the triangle is 898 - (250 + 435) = <<898-(250+435)=108>>108m. ### Answer: 108
Expected answer: 213
Correct? No
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. Let x be the length of one side. The perimeter of the triangle is 3x. 3x = 405 x = 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let's call the length of one of the sides of the triangle "s". The perimeter of the triangle is 3s. The total perimeter of the triangle is 612 meters. 3s = 612 s = 612/3 = <<612/3=204>>204 meters The length of each side of the triangle is 204 meters. ### Answer: 204
Expected answer: 204
Correct? Yes
Problem: An equilateral triangle has a perimeter of 591 cm. Can you find the length of each side of this triangle?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. 3 times the length of one side = 591 cm. The length of one side = 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 858 x = 858/3 = <<858/3=286>>286 Each of the sides of the triangle is 286m long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 543 x = 543/3 = <<543/3=181>>181 Each of the sides of the triangle is 181 meters long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of each 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.
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. The length of each side of this 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 129 x = 129/3 = <<129/3=43>>43 Each of the sides of the triangle is 43m long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 858 x = 858/3 = <<858/3=286>>286 Each of the sides of the triangle is 286 meters long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. The length of one of its sides is 513/3 = <<513/3=171>>171 km. ### Answer: 171
Expected answer: 171
Correct? Yes
Problem: A triangular field has a perimeter of 828 meters. Two sides of the field are 105 and 434 meters long. How long is the third side of the field?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. Let x be the length of the third side. 37 + 559 + x = 773 x = 773 - 37 - 559 x = <<773-37-559=249>>249 cm ### Answer: 249
Expected answer: 177
Correct? No
Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 714 x = 714/3 = <<714/3=238>>238 Each of the sides of the triangle is 238m long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The perimeter of the garden is 792m. The length of the first side is 147m. The length of the second side is 590m. The length of the third side is <<147+590+x=792>>x=<<147+590+x=792>>792-637=<<147+590+x=792>>792-637=<<147+590+x=792>>155 ### Answer: 155
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. The length of the third side is 871 - (321 + 528) = <<871-(321+528)=871-849=22>>22 meters. ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: A triangle has a perimeter of 991m. Two sides of the triangle measure 424m and 246m respectively. Find the length of the third side of the triangle.
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. The length of the third side of the triangle is 991-424-246 = <<991-424-246=221>>221m. ### Answer: 221
Expected answer: 321
Correct? No
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Each side of the triangle is 936/3 = <<936/3=312>>312m. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. The length of the third side of the triangle is 721 - (204 + 195) = <<721-(204+195)=721-409=312>>312 m. ### Answer: 312
Expected answer: 322
Correct? No
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 201m Length of one of its sides = 201/3 = <<201/3=67>>67m ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3s = 756 s = 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The perimeter of the triangle is 735+144+x = <<735+144+x=923>>923. 735+144+x = 923 x = 923-735-144 x = <<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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 813 x = 813/3 = <<813/3=271>>271 cm Each of the sides of the triangle is 271 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 834 x = 834/3 = <<834/3=278>>278 feet. Each of the sides of the triangle is 278 feet long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The perimeter of the triangle is 105m. The length of one side of the triangle 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Since all sides of the triangle are equal, the perimeter of the triangle is 3 times the length of each side. 3 times the length of each side = 195cm. The length of each side = 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?
LLemma 7B:
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)=221>>221m. ### Answer: 221
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The length of the third side is 989-128-288 = <<989-128-288=583>>583m. ### Answer: 583
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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. 321 = 3 * <<321/3=107>>107 Each side of the triangle is 107 meters long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 258 x = 258/3 = <<258/3=86>>86 cm Each of the sides of the triangle is 86 cm long. ### 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?
LLemma 7B:
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 <<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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The perimeter of the triangle is 620+80+x = <<620+80+x=700+x>>700+x. 700+x = 979 x = <<979-700=279>>279 The length of the third side is 279m. ### Answer: 279
Expected answer: 279
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966 meters. What is the length of each side of this triangle?
LLemma 7B:
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 <<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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 486 cm. The length of one of its sides = 486/3 = <<486/3=162>>162 cm. Each of its sides is 162 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 948 x = 948/3 = <<948/3=316>>316 Each of the sides of the triangle is 316 meters long. ### 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?
LLemma 7B:
Reasoning: The total perimeter of the triangle is 252+687+<<third side>>. 998 = 252+687+<<third side>> <<third side>> = 998-252-687 = <<third side>> = 998-949 = <<third side>> = 49 ### Answer: 49
Expected answer: 59
Correct? No
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 3 times the length of each of its sides = 3 times 618 = <<3*618=1854>>1854m The length of each of its sides is 1854m. ### Answer: 1854
Expected answer: 206
Correct? No
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. Each side is 483/3 = <<483/3=161>>161 meters long. ### Answer: 161
Expected answer: 161
Correct? Yes
Problem: A triangle has a perimeter of 804m. One of its sides is 262m long and another is 90m long. What is the length of the third side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The perimeter of the triangle is 183+498+x=925. 183+498+x=925 x=925-183-498 x=925-671 x=254 ### Answer: 254
Expected answer: 244
Correct? No
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?
LLemma 7B:
Reasoning: The sum of the lengths of the sides of a triangle is 573m. The sum of the lengths of the sides of a triangle is 573m. The length of the third side is 573-103-386 = <<573-103-386=174>>174m. ### Answer: 174
Expected answer: 84
Correct? No
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 330m. 3x = 330 x = 330/3 = <<330/3=110>>110m Each of its sides is 110m long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 850 - (57 + 426) = <<850-(57+426)=850-483=367>>367m. ### Answer: 367
Expected answer: 367
Correct? Yes
Problem: A triangle has a perimeter of 764m. Two of its sides are 265m and 56m in length. What is the length of the third side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 764 - 265 - 56 = <<764-265-56=243>>243m. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 723 x = 723/3 = <<723/3=241>>241 Each of the triangle's sides is 241cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The perimeter of the triangle is 315+100+<<third side>>. 738=315+100+<<third side>> <<third side>>=<<738-315-100=323>>323 ### Answer: 323
Expected answer: 323
Correct? Yes
Problem: A triangle has a perimeter of 762m. If one of the sides measures 131m, and the other side is 147m long, what is the length of the third side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. The length of the third side is 762 - (131 + 147) = <<762-(131+147)=184>>184m. ### Answer: 184
Expected answer: 484
Correct? No
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?
LLemma 7B:
Reasoning: The sum of the lengths of the two sides is 472m. The perimeter of the triangle is 784m. 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 543 x = 543/3 = <<543/3=181>>181 Each of the sides of the triangle is 181mm. ### 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?
LLemma 7B:
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=105>>105m. ### Answer: 105
Expected answer: 105
Correct? Yes
Problem: The perimeter of a triangle is 934m. The lengths of two of its sides add up to 838m (one is 828m and the other is 10m). What is the length of the third side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. The lengths of two of its sides add up to 838m. The length of the third side is 838-828-10 = <<838-828-10=10>>10m. The length of the third side is 10m. ### Answer: 10
Expected answer: 96
Correct? No
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The perimeter of the triangle is 109+530+x = <<109+530+x=677>>677. x = <<677-109-530=0>>0. ### Answer: 0
Expected answer: 38
Correct? No
Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 582 x = 582/3 = <<582/3=194>>194 cm Each of the sides of the triangle is 194 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the last side is 499 - 259 - 11 = <<499-259-11=129>>129m. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 966m 3 times the length of one of its sides = 966/3 = <<966/3=322>>322m The length of each of its sides is 322m. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 894 inches. What is the length of each side of the triangle?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. 3 times the length of one side = 894 inches. The length of one side = 894/3 = <<894/3=298>>298 inches. Each side of the triangle is 298 inches long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 891 x = 891/3 = <<891/3=297>>297cm Each of the sides of the triangle is 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of each side. 3 times the length of each side = 411m The length of each side = 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?
LLemma 7B:
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The perimeter of the triangle is 537+68+x = <<537+68+x=930>>930 meters. 930-537-68 = <<930-537-68=295>>295 meters is the length of the third side. ### Answer: 295
Expected answer: 325
Correct? No
Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 657 x = 657/3 = <<657/3=219>>219 meters Each of the sides of the triangle is 219 meters long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The perimeter of the triangle is 368+230+x = <<368+230+x=909>>909. 909-368-230 = <<909-368-230=311>>311+x = <<311+x=909>>909. x = <<909-311=598>>598. The length of the third side is 598m. ### Answer: 598
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 700 - (140 + 525) = <<700-(140+525)=185>>185 m. ### Answer: 185
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The perimeter of the triangle is 484+130+x = 915. 484+130+x = 915 x = 915-484-130 x = 915-614 x = <<915-614=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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Each side of the triangle is 120/3 = <<120/3=40>>40 cm. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A triangular field has a perimeter of 661m. Two sides of the field are known to be 382m and 151m respectively. What is the length of the third side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. The third side is 661-382-151 = <<661-382-151=138>>138m. ### Answer: 138
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of its three sides. The length of the third side is 678 - (419 + 164) = <<678-(419+164)=191>>191 feet. ### Answer: 191
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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. The perimeter of the triangle is 186+37+x = <<186+37+x=223+x>>223+x. 223+x = 248 x = 248-223 x = <<248-223=25>>25 The length of the remaining side is 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 246 x = 246/3 = <<246/3=82>>82 Each of the sides of the triangle is 82 centimeters long. ### 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.
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. The total perimeter of a triangular field is 739 meters. The length of the first side is 180 meters. The length of the second side is 338 meters. The length of the third side is <<180+338=518>>518 meters. ### Answer: 518
Expected answer: 221
Correct? No
Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 684cm. The length of one of its sides = 684/3 = <<684/3=228>>228cm. Each of its sides is 228cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 537 x = 537/3 = <<537/3=179>>179 Each of the sides of the triangle is 179m. ### Answer: 179
Expected answer: 179
Correct? Yes
Problem: A triangle has a perimeter of 568m. The lengths of two of its sides are 110m and 205m. What is the length of the third side?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The length of the third side is 568 - 110 - 205 = <<568-110-205=253>>253m. ### Answer: 253
Expected answer: 253
Correct? Yes
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 942mm. The length of one of its sides = 942/3 = <<942/3=314>>314mm. Each of its sides is 314mm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The perimeter of the triangle is 325+15+x = <<325+15+x=340+x>>340+x meters. The total perimeter of the triangle is 633 meters. 340+x = <<340+x=633>>633 x = <<633-340=293>>293 meters. ### Answer: 293
Expected answer: 293
Correct? Yes
Problem: An equilateral triangle has a perimeter of 504 meters. What is the length of each side of the triangle?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. 3 times the length of one side = 504 Length of one side = <<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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. The perimeter of the triangle is 3x. 3x = 51 x = <<51/3=17>>17 Each of the sides of the triangle is 17 cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one side. 3 times the length of one side = 501 The length of one side = 501/3 = <<501/3=167>>167 feet. ### Answer: 167
Expected answer: 167
Correct? Yes
Problem: The perimeter of an equilateral triangle is 411 meters. What is the length of each side of the triangle?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of each side. Let x be the length of each side of the triangle. The perimeter of the triangle is 3x. 3x = 411 x = 411/3 = <<411/3=137>>137 Each side of the triangle is 137 meters. ### Answer: 137
Expected answer: 137
Correct? Yes
Problem: An equilateral triangle has a perimeter of 114cm. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. Let x be the length of one of its sides. Then the perimeter is 3x. 3x = 114 x = 114/3 = <<114/3=38>>38 Each of its sides is 38cm long. ### 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?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 69m The length of one of its sides = 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?
LLemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. The perimeter of the triangle is 464+377+x=907. 464+377+x=907 x=907-464-377 x=<<907-464-377=156>>156m ### Answer: 156
Expected answer: 66
Correct? No
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
LLemma 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of one of its sides. 3 times the length of one of its sides = 966m 3 times the length of one of its sides = 966/3 = <<966/3=322>>322m The length of each of its sides is 322m. ### Answer: 322
Expected answer: 322
Correct? Yes