LLemma 34B on 3.MD.D.8-quadrilateral
Common Core Standard 3.MD.D.8-quadrilateral
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: The perimeter of a rectangular swimming pool is 324 meters. The length of the pool is 83 meters. What is the width of the pool?
LLemma 34B:
Reasoning: The perimeter of a rectangle is 2*length + 2*width. 324 = 2*83 + 2*width 324 = 166 + 2*width 324 - 166 = 2*width 158 = 2*width 158/2 = <<158/2=79>>79 = width ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 40m. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 40/4 = <<40/4=10>>10 ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: A square has a perimeter of 344m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 344/4 = <<344/4=86>>86 ### Answer: 86
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 348m. What would be the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 348/4 = <<348/4=87>>87 ### Answer: 87
Expected answer: 87
Correct? Yes
Problem: A rectangle has a perimeter of 194 cm. The length of one of its sides is 49 cm. Can you determine the length of its other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle
Expected answer: 48
Correct? No
Problem: A square has a perimeter of 192m. What is the length of one side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 192/4 = <<192/4=48>>48 ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 68/4 = <<68/4=17>>17 ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: A rectangle has a perimeter of 52 meters. If one of the sides measures 4 meters, how long is the other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle
Expected answer: 22
Correct? No
Problem: A quadrilateral has a perimeter of 229m. Two sides of the quadrilateral have lengths of 93m and 98m respectively. The third side of the quadrilateral is 36m long. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 229m. The perimeter of the quadrilateral is 93m+98m+36m+x = <<93+98+36+x>>229m. 229m = 229m. x = <<229-93-98-36>>0m. The length of the fourth side is 0m. ### Answer: 0m
Expected answer: 2
Correct? No
Problem: The perimeter of a square is 16m. What is the length of each side of this square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 16/4 = <<16/4=4>>4 ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: A square has a perimeter of 272m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 272/4 = <<272/4=68>>68 ### Answer: 68
Expected answer: 68
Correct? Yes
Problem: A square has a perimeter of 244m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 244/4 = <<244/4=61>>61 ### Answer: 61
Expected answer: 61
Correct? Yes
Problem: A quadrilateral has a perimeter of 227m. The lengths of three of its sides are 70m, 29m, and 61m. What is the length of the fourth side of the quadrilateral?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 227m. The lengths of three of its sides are 70m, 29m, and 61m. The length of the fourth side of the quadrilateral is 227-70-29-61 = <<227-70-29-61=67>>67m. ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 280m. What is the length of the side of that square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of the side. The length of the side of the square is 280/4 = <<280/4=70>>70m. ### Answer: 70
Expected answer: 70
Correct? Yes
Problem: A quadrilateral has a perimeter of 219cm. Two of its sides have lengths of 37cm and 98cm, and a third side is known to be 41cm. How long is the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its sides. The fourth side is 219-37-98-41 = <<219-37-98-41=43>>43cm. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 44/4 = <<44/4=11>>11 ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: A rectangular garden has a perimeter of 282 meters. The longer side measures 71 meters. What is the length of the shorter side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of the lengths of the sides. The perimeter of the garden is 282 meters. The longer side measures 71 meters. The shorter side measures 282/2 - 71 = <<282/2-71=111>>111 meters. ### Answer: 111
Expected answer: 70
Correct? No
Problem: A rectangular garden has a total perimeter of 128 meters. If the shorter side of the garden has a length of 57 meters, how long is the other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is 2*length + 2*width. The perimeter of the garden is 128 = 2*57 + 2*width. 128 = 114 + 2*width. 128 - 114 = 2*width. 14 = 2*width. 14/2 = <<14/2=7>>7 = width. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 392m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 392/4 = <<392/4=98>>98 ### Answer: 98
Expected answer: 98
Correct? Yes
Problem: A rectangle has a perimeter of 204m. If one of its sides has a length of 16m, what is the length of the other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle
Expected answer: 86
Correct? No
Problem: A square has a perimeter of 336cm. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. 336/4 = <<336/4=84>>84 ### Answer: 84
Expected answer: 84
Correct? Yes
Problem: A square has a perimeter of 144 meters. What is the length of one side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 144/4 = <<144/4=36>>36 meters is the length of one side of the square. ### Answer: 36
Expected answer: 36
Correct? Yes
Problem: A quadrilateral has a perimeter of 236 cm. Two of its sides measure 69 cm and 50 cm respectively, and a third side measures 39 cm. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 236 cm. The perimeter of the quadrilateral is 69+50+39+x = <<69+50+39+x=158+x>>158+x cm. The length of the fourth side is 236-158 = <<236-158=78>>78 cm. ### Answer: 78
Expected answer: 78
Correct? Yes
Problem: A quadrilateral has a perimeter of 193cm. Two of its sides measure 37cm and 14cm, while the other two sides measure 73cm and an unknown length. What is the length of the side of the quadrilateral that is unknown?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 193cm. The perimeter of the quadrilateral is 37+14+73+x = <<37+14+73+x=124+x>>124+x. 124+x = 193 x = 193-124 = <<193-124=69>>69 ### Answer: 69
Expected answer: 69
Correct? Yes
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. The length of one of its sides is 160/4 = <<160/4=40>>40m. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A rectangle has a perimeter of 228 meters. The length of the rectangle is 90 meters. What is the width of the rectangle?
LLemma 34B:
Reasoning: The perimeter of a rectangle is 2(length + width). 228 = 2(90 + width) 228 = 180 + 2width 48 = 2width 24 = width ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: The perimeter of a square field is 136 meters. Given that all sides are equal in a square, What is the length of one side of the field?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 136/4 = <<136/4=34>>34 meters is the length of one side of the field. ### Answer: 34
Expected answer: 34
Correct? Yes
Problem: A rectangle has a total perimeter of 236 meters. If one side of the rectangle is 43 meters, can you determine the length of the opposite side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle
Expected answer: 75
Correct? No
Problem: A quadrilateral has a perimeter of 206m. Two of its sides together have a length of 58m, and the other two sides together have a length of 54m and 1m, respectively. What is the length of the missing portion of the perimeter?
LLemma 34B:
Reasoning: The missing portion of the perimeter is 206-58-54-1 = <<206-58-54-1=83>>83m. ### Answer: 83
Expected answer: 93
Correct? No
Problem: A square field has a total perimeter of 284 meters. How long is each side of the square field?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 284/4 = <<284/4=71>>71 meters is the length of each side of the square field. ### Answer: 71
Expected answer: 71
Correct? Yes
Problem: A rectangle has a perimeter of 150 feet. If the length of the rectangle is 69 feet, what is the width of the rectangle?
LLemma 34B:
Reasoning: The width of the rectangle is 150-69 = <<150-69=81>>81 feet. ### Answer: 81
Expected answer: 6
Correct? No
Problem: The perimeter of a rectangle is 166m. If one of the sides measures 35m, how long is the other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The other side is 166-35 = <<166-35=131>>131m. ### Answer: 131
Expected answer: 48
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 124/4 = <<124/4=31>>31 ### Answer: 31
Expected answer: 31
Correct? Yes
Problem: A rectangular field has a perimeter of 336 feet. The length of one of its sides is 79 feet. What is the length of the opposite side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of its length and width. Let x be the width of the rectangle. 2(79+x) = 336 158+2x = 336 2x = 178 x = 89 The width of the rectangle is 89 feet. ### Answer: 89
Expected answer: 89
Correct? Yes
Problem: A square plot of land has a perimeter of 132 meters. What is the length of one side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 132/4 = <<132/4=33>>33 meters is the length of one side of the square. ### Answer: 33
Expected answer: 33
Correct? Yes
Problem: A rectangle has a perimeter of 138 feet. If the length of the rectangle is 46 feet, what is the width of the rectangle?
LLemma 34B:
Reasoning: The width of the rectangle is 138-2*46 = <<138-2*46=26>>26 feet. ### Answer: 26
Expected answer: 23
Correct? No
Problem: A rectangular field has a total perimeter of 200 meters. The length of the field is known to be 49 meters. What is the width of the field in meters?
LLemma 34B:
Reasoning: The width of the field is 200-2*49 = <<200-2*49=92>>92 meters. ### Answer: 92
Expected answer: 51
Correct? No
Problem: A square has a perimeter of 200m. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 200/4 = <<200/4=50>>50 ### Answer: 50
Expected answer: 50
Correct? Yes
Problem: A quadrilateral has a perimeter of 199m. The length of one side is 9m, the length of the second side is 30m, and the length of the third side is 71m. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its sides. The length of the fourth side is 199-9-30-71 = <<199-9-30-71=89>>89m. ### Answer: 89
Expected answer: 89
Correct? Yes
Problem: A quadrilateral has a perimeter of 207m. The lengths of three of its sides are 35m, 62m and 70m respectively. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 207m. The lengths of three of its sides are 35m, 62m and 70m respectively. The length of the fourth side is 207-35-62-70 = <<207-35-62-70=40>>40m. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A rectangle has a perimeter of 384cm. If one of the shorter sides of the rectangle is measured to be 99cm, what would be the length of the longer sides of the rectangle?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice the sum of the lengths of the shorter sides. The perimeter of a rectangle is twice
Expected answer: 93
Correct? No
Problem: A quadrilateral shape has a perimeter of 255 m. The first and the second sides have lengths of 78m and 15m respectively, while the third side has a length of 63m. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its sides. The length of the fourth side is 255-78-15-63 = <<255-78-15-63=99>>99 m. ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: A square has a perimeter of 128m. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. 128/4 = <<128/4=32>>32 ### Answer: 32
Expected answer: 32
Correct? Yes
Problem: Imagine a rectangle with a perimeter of 96 feet. You know that one pair of opposite sides are each 33 feet long. Can you find the length of the other pair of opposite sides?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle is twice the sum of the lengths of its sides. The perimeter of a rectangle
Expected answer: 15
Correct? No
Problem: The perimeter of a square field is 112 meters. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 112/4 = <<112/4=28>>28 meters is the length of each side. ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: The perimeter of a square is 32 cm. Can you find the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. 32/4 = <<32/4=8>>8 cm is the length of one of its sides. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 364m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 364/4 = <<364/4=91>>91 ### Answer: 91
Expected answer: 91
Correct? Yes
Problem: The total perimeter of a rectangle is found to be 144 feet. The length of one side is known to be 38 feet. What is the length of the other side of the rectangle in feet?
LLemma 34B:
Reasoning: The perimeter of a rectangle is 2*length + 2*width. 144 = 2*38 + 2*width 144 = 76 + 2*width width = (144-76)/2 = <<(144-76)/2=38>>38 ### Answer: 38
Expected answer: 34
Correct? No
Problem: A quadrilateral has a perimeter of 205m. Two of its sides add up to 54m and the other two sides add up to 22m and 37m respectively. What is the length of the remaining side to complete the perimeter?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 205m. The perimeter of the quadrilateral is 54m+22m+37m+x = <<54+22+37+x>>113+x 113+x = 205 x = 205-113 = <<205-113=92>>92 ### Answer: 92
Expected answer: 92
Correct? Yes
Problem: The perimeter of a rectangular field is 174m. If the length of the field is 65m, what is the width of the field?
LLemma 34B:
Reasoning: The perimeter of a rectangle is 2(length + width). 174 = 2(65 + width) 174 = 130 + 2width 44 = 2width 22 = width ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: A quadrilateral has a perimeter of 176 cm. The lengths of three sides are 25 cm, 17 cm and 89 cm respectively. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its four sides. The length of the fourth side is 176-25-17-89 = <<176-25-17-89=55>>55 cm. ### Answer: 55
Expected answer: 45
Correct? No
Problem: A square has a perimeter of 372 meters. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 372/4 = <<372/4=93>>93 meters is the length of each side. ### Answer: 93
Expected answer: 93
Correct? Yes
Problem: A square field has a perimeter of 240 meters. Can you find out the length of one side of the field?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 240/4 = <<240/4=60>>60 meters is the length of one side of the field. ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: The perimeter of a rectangle is 242 meters. Knowing that one of the sides of this rectangle is 97 meters, can you determine the length of the other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of this rectangle is 242 meters. The length of one side is 97 meters. The length of the other side is 242-97 = <<242-97=145>>145 meters. ### Answer: 145
Expected answer: 24
Correct? No
Problem: Tom has constructed a square with a total perimeter of 316 meters. Can you determine the length of each side of this square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 316/4 = <<316/4=79>>79 meters is the length of each side of the square. ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 268cm. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 268/4 = <<268/4=67>>67 ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 348m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 348/4 = <<348/4=87>>87 ### Answer: 87
Expected answer: 87
Correct? Yes
Problem: A square has a perimeter of 400m. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. The length of one of its sides is 400/4 = <<400/4=100>>100m. ### Answer: 100
Expected answer: 100
Correct? Yes
Problem: A quadrilateral has sides with lengths of 81m, 100m, and 19m. If its perimeter is 243m, what is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its sides. The length of the fourth side is 243-81-100-19 = <<243-81-100-19=43>>43m. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: A rectangle has a perimeter of 186cm. If one of its sides is 50cm long, how long is the other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle is twice the sum of its sides. The perimeter of a rectangle
Expected answer: 43
Correct? No
Problem: A rectangle has a perimeter of 224 cm. If the length of one of its sides is 78 cm, what is the length of the adjacent side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of its sides. The length of the adjacent side is 224-78 = <<224-78=146>>146 cm. ### Answer: 146
Expected answer: 34
Correct? No
Problem: A quadrilateral has two sides measuring 79m and 97m. Another side measures 51m. The total perimeter of the quadrilateral is 235m. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 79+97+51+x = 235. 79+97+51+x = 235 227+x = 235 x = 235-227 x = <<235-227=8>>8 ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 28/4 = <<28/4=7>>7 ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 48cm. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 48/4 = <<48/4=12>>12 ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: A square plot of land has a perimeter of 184 meters. Can you find the length of one side of the plot?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 184/4 = <<184/4=46>>46 meters is the length of one side of the plot. ### Answer: 46
Expected answer: 46
Correct? Yes
Problem: A square has a perimeter of 56 meters. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 56/4 = <<56/4=14>>14 meters is the length of each side. ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: A quadrilateral has a perimeter of 157m. If one of its sides is 97m long, and the other two sides are 5m and 30m, respectively, what is the length of the fourth side to complete the perimeter?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 157m. The perimeter of the quadrilateral is 97m + 5m + 30m + x = <<97+5+30+x=157>>157m. x = <<157-97-5-30=25>>25m. ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: A quadrilateral has a perimeter of 173m. The length of the first side is 46m, second side is 50m and third side is 35m. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its sides. The length of the fourth side is 173-46-50-35 = <<173-46-50-35=42>>42m. ### Answer: 42
Expected answer: 42
Correct? Yes
Problem: A square has a perimeter of 72 cm. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. The length of one of its sides is 72/4 = <<72/4=18>>18 cm. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: A square has a perimeter of 352m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 352/4 = <<352/4=88>>88 ### Answer: 88
Expected answer: 88
Correct? Yes
Problem: A rectangle has 23m for its length and has a total perimeter of 116m. What is the length of its width?
LLemma 34B:
Reasoning: The width of the rectangle is 116-23-23 = <<116-23-23=60>>60m. ### Answer: 60
Expected answer: 35
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 124/4 = <<124/4=31>>31 ### Answer: 31
Expected answer: 31
Correct? Yes
Problem: A quadrilateral has a total perimeter of 131m. Three of its sides have lengths 24m, 57m, and 17m respectively. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 131m. The perimeter of the quadrilateral is 24m+57m+17m+x = <<24+57+17+x>>108+x. 108+x = 131 x = 131-108 = <<131-108=23>>23 The length of the fourth side is 23m. ### Answer: 23
Expected answer: 33
Correct? No
Problem: A rectangle has a perimeter of 254m. One of its sides has a length of 89m. What is the length of the other side?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the sum of its sides. 254 = 2(89+x) 254 = 178+2x 76 = 2x 38 = x ### Answer: 38
Expected answer: 38
Correct? Yes
Problem: A square has a perimeter of 208m. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 208/4 = <<208/4=52>>52 ### Answer: 52
Expected answer: 52
Correct? Yes
Problem: A square has a perimeter of 64m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 64/4 = <<64/4=16>>16 is the length of each side of the square. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: A quadrilateral has a total perimeter of 196 meters. The lengths of three of its sides combined is 183 meters (with one side being 92 meters and the other two sides being 29 and 62 meters respectively). Can you figure out the length of the fourth side?
LLemma 34B:
Reasoning: The length of the fourth side is 196-183 = <<196-183=13>>13 meters. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: The perimeter of a quadrilateral is 191 units. If one side is 35 units in length, another side is 76 units, and the third side is 5 units, what is the length of the fourth side in units?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is 191 units. If one side is 35 units in length, another side is 76 units, and the third side is 5 units, then the length of the fourth side is 191-35-76-5 = <<191-35-76-5=75>>75 units. ### Answer: 75
Expected answer: 75
Correct? Yes
Problem: A square has a perimeter of 104m. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 104/4 = <<104/4=26>>26 ### Answer: 26
Expected answer: 26
Correct? Yes
Problem: The perimeter of a rectangle is 198 cm. If the length of this rectangle is 90 cm, what is the width?
LLemma 34B:
Reasoning: The perimeter of a rectangle is 2(length + width). 2(90 + width) = 198 180 + 2width = 198 2width = 198 - 180 2width = 18 width = 18/2 width = <<18/2=9>>9 ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Jack is designing a rectangular garden with a total perimeter of 128 feet. He has already planned for one pair of opposite sides to be 47 feet each. What should be the length of the remaining two opposite sides?
LLemma 34B:
Reasoning: The perimeter of the garden is 128 feet. The perimeter of the garden is the sum of the lengths of all four sides. The perimeter of the garden is 47+47+x+x = <<47+47+x+x=94+2x>>94+2x. 94+2x = 128 2x = 128-94 2x = <<128-94=34>>34 x = <<34/2=17>>17 The length of the remaining two opposite sides is 17 feet. ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: A square has a perimeter of 356m. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. 356/4 = <<356/4=89>>89 ### Answer: 89
Expected answer: 89
Correct? Yes
Problem: A quadrilateral has a perimeter of 236 units. Two sides of the quadrilateral measure 89 units and 87 units respectively, while the third side is 1 unit long. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of the quadrilateral is 236 units. The perimeter of the quadrilateral is 89+87+1+x = <<89+87+1+x=236>>236 units. x = <<236-89-87-1=59>>59 units. ### Answer: 59
Expected answer: 59
Correct? Yes
Problem: A square has a perimeter of 340 meters. What is the length of each side of this square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 340/4 = <<340/4=85>>85 meters is the length of each side of this square. ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: A square has a perimeter of 16m. What is the length of each side?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 16/4 = <<16/4=4>>4 ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: A quadrilateral has four sides. The length of the first side is 1m, the second side is 54m, and the third side is 9m. The total perimeter of this quadrilateral is 81m. What would be the length of the fourth side in meters?
LLemma 34B:
Reasoning: The length of the fourth side is 81-1-54-9 = <<81-1-54-9=17>>17m. ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: A quadrilateral, which is a perfect square, has a total perimeter of 316m. What is the length of each side of this square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 316/4 = <<316/4=79>>79 ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 300m. How long is each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 300/4 = <<300/4=75>>75 ### Answer: 75
Expected answer: 75
Correct? Yes
Problem: A quadrilateral has a perimeter of 198m. Two of the sides have lengths of 19m and 57m respectively, another side is 22m, what is the length of the remaining side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its sides. The perimeter of the quadrilateral is 198m. The sum of the lengths of the three known sides is 19m+57m+22m = <<19+57+22=98>>98m. The length of the remaining side is 198m-98m = <<198-98=100>>100m. ### Answer: 100
Expected answer: 100
Correct? Yes
Problem: A square has a perimeter of 172m. What is the length of each side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of each side. 172/4 = <<172/4=43>>43 ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. The length of one of its sides is 304/4 = <<304/4=76>>76 cm. ### Answer: 76
Expected answer: 76
Correct? Yes
Problem: A rectangle has a total perimeter of 158 meters. Each of the shorter sides is 51 meters long. What is the length of each of the longer sides?
LLemma 34B:
Reasoning: The perimeter of a rectangle is twice the length of the longer side plus twice the length of the shorter side. 158 = 2*x + 2*51 158 = 2*x + 102 158 - 102 = 2*x 56 = 2*x 56/2 = x 28 = x ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: A square has a perimeter of 72m. What is the length of one its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. The length of one of its sides is 72/4 = <<72/4=18>>18m. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: A rectangular playground is bordered by a fence. Two opposite sides of the fence are 19m each. If the total length of the fence is 166m, what is the length of each of the other two sides?
LLemma 34B:
Reasoning: The length of each of the other two sides is 166-19-19 = <<166-19-19=138>>138m. ### Answer: 138
Expected answer: 64
Correct? No
Problem: A quadrilateral has a perimeter of 246m. You know that two of its sides are 40m and 32m long, another side is 95m long. What is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its sides. The length of the fourth side is 246-40-32-95 = <<246-40-32-95=25>>25m. ### Answer: 25m
Expected answer: 79
Correct? No
Problem: A square has a perimeter of 32m. What is the length of one of its sides?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one of its sides. The length of one of its sides is 32/4 = <<32/4=8>>8m. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 12 meters. Can you find the length of one side of the square?
LLemma 34B:
Reasoning: The perimeter of a square is 4 times the length of one side. 12/4 = <<12/4=3>>3 meters is the length of one side of the square. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: A quadrilateral has a perimeter of 160m. If the three known sides have lengths of 29m, 16m, and 41m, what is the length of the fourth side?
LLemma 34B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its four sides. The length of the fourth side is 160-29-16-41 = <<160-29-16-41=74>>74m. ### Answer: 74m
Expected answer: 74
Correct? Yes
Problem: A rectangle has a perimeter of 98m. If one of its sides is 5m long, what is the length of the other side?
LLemma 34B:
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Expected answer: 44
Correct? No
Problem: A rectangle has two sides measuring 45m each. If the total perimeter of the rectangle is 210m, what is the length of each of the other two sides?
LLemma 34B:
Reasoning: The perimeter of the rectangle is 210m. The perimeter of the rectangle is 2(45+x) = <<2(45+x)=90+2x>>90+2x. 210 = 90+2x <<210=90+2x>>210 = 90+2x <<210-90=2x>>210-90 = 2x <<120=2x>>120 = 2x <<120/2=x>>120/2 = x <<60=x>>60 = x The length of each of the other two sides is 60m. ### Answer: 60
Expected answer: 60
Correct? Yes