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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. We can rearrange this formula to solve for W: W = (P/2) - L. Substituting the given values, we get W = (324/2) - 83 = <<(324/2)-83=88>>88 meters. ### Answer: 88
Expected answer: 79
Correct? No
Problem: A square has a perimeter of 40m. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 40m / 4 = <<40/4=10>>10m ### Answer: 10m
Expected answer: 10
Correct? Yes
Problem: A square has a perimeter of 344m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 344m / 4 = <<344/4=86>>86m ### Answer: 86m
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 348m. What would be the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 348m / 4 = <<348/4=87>>87m ### Answer: 87m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 194 cm and one side (let's assume it's the length) is 49 cm, we can set up the equation 194 = 2(49 + w). Solving for w, we get w = (194/2) - 49 = <<(194/2)-49=48>>48 cm. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 192m. What is the length of one side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Let x be the length of one side. 4x = 192 x = <<192/4=48>>48 The length of one side is 48m. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side is 68/4 = <<68/4=17>>17cm. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 52 meters and one side (let's assume it's the width) is 4 meters, we can set up the equation 52 = 2(l + 4). Solving for l, we get l = (52/2) - 4 = 26 - 4 = <<26-4=22>>22 meters. ### Answer: 22
Expected answer: 22
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all four sides. Therefore, the length of the fourth side is 229 - (93 + 98 + 36) = <<229-(93+98+36)=12>>12m. ### Answer: 12m
Expected answer: 2
Correct? No
Problem: The perimeter of a square is 16m. What is the length of each side of this square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 16m / 4 = <<16/4=4>>4m ### Answer: 4m
Expected answer: 4
Correct? Yes
Problem: A square has a perimeter of 272m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 272m / 4 = <<272/4=68>>68m ### Answer: 68m
Expected answer: 68
Correct? Yes
Problem: A square has a perimeter of 244m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 244m / 4 = <<244/4=61>>61m ### Answer: 61m
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?
Qwen2-Math 7B:
Reasoning: 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side 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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all four sides. Let's denote the length of the fourth side as x. We have the equation: 37 + 98 + 41 + x = 219 Solving for x, we get: x = 219 - (37 + 98 + 41) = <<219-(37+98+41)=43>>43 Therefore, the length of the fourth side is 43cm. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 44m / 4 = <<44/4=11>>11m ### Answer: 11m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 282 meters and the length is 71 meters, we can set up the equation 282 = 2(71 + w). Solving for w, we get w = (282/2) - 71 = <<(282/2)-71=70>>70 meters. ### Answer: 70
Expected answer: 70
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Since the perimeter is 128 meters and one side (the shorter side) is 57 meters, we can set up the equation 128 = 2(57 + w). Solving for w, we get w = (128 - 2*57) / 2 = <<(128 - 2*57) / 2=17>>17 meters. The other side of the garden is 17 meters long. ### Answer: 17
Expected answer: 7
Correct? No
Problem: A square has a perimeter of 392m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 392m / 4 = <<392/4=98>>98m ### Answer: 98m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 204m and one side (let's assume it's the width) is 16m, we can set up the equation 204 = 2(16 + w). Solving for w, we get w = (204/2) - 16 = 102 - 16 = <<102-16=86>>86m. ### Answer: 86m
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 336cm. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side is 336/4 = <<336/4=84>>84cm. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 144/4 = <<144/4=36>>36 The length of one side of the square is 36 meters. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all four sides. Let's denote the length of the fourth side as x. Then, we have: 69 + 50 + 39 + x = 236 158 + x = 236 x = 236 - 158 x = <<236-158=78>>78 The length of the fourth side is 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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of all its sides. Therefore, the unknown side can be found by subtracting the sum of the known sides from the perimeter. The sum of the known sides is 37+14+73 = <<37+14+73=124>>124cm. The unknown side is 193-124 = <<193-124=69>>69cm. ### Answer: 69
Expected answer: 69
Correct? Yes
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side is 160/4 = <<160/4=40>>40m. ### Answer: 40m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. Substituting the given values, we have 228 = 2(90 + W). Solving for W, we get W = (228/2) - 90 = <<(228/2)-90=12>>12 meters. ### Answer: 12
Expected answer: 24
Correct? No
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since all sides are equal, we can find the length of one side by dividing the perimeter by 4. 136/4 = <<136/4=34>>34 ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that one side (let's assume it's the width) is 43 meters, and the perimeter is 236 meters, we can set up the equation as follows: 236 = 2(43 + w). Simplifying, we get 236 = 86 + 2w, which leads to 2w = 150, and thus w = 75 meters. Therefore, the length of the opposite side is 75 meters. ### Answer: 75
Expected answer: 75
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all its sides. We know that two sides have a combined length of 58m, and the other two sides have lengths of 54m and 1m, respectively. Therefore, the length of the missing portion of the perimeter is 206 - (58 + 54 + 1) = <<206-(58+54+1)=93>>93m. ### Answer: 93m
Expected answer: 93
Correct? Yes
Problem: A square field has a total perimeter of 284 meters. How long is each side of the square field?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, each side of the square field is 284/4 = <<284/4=71>>71 meters long. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. Substituting the given values, we have 150 = 2(69 + W). Solving for W, we get W = (150/2) - 69 = <<(150/2)-69=15>>15 feet. ### Answer: 15
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 166m and one side (let's assume it's the width) is 35m, we can set up the equation 166 = 2(35 + l). Solving for l, we get l = (166/2) - 35 = <<(166/2)-35=48>>48m. The other side of the rectangle is 48m long. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 124m / 4 = <<124/4=31>>31m ### Answer: 31m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. Given that the perimeter is 336 feet and one side (length) is 79 feet, we can find the width by rearranging the formula: W = (P/2) - L = (336/2) - 79 = <<(336/2)-79=88>>88 feet. The length of the opposite side is also 88 feet. ### Answer: 88
Expected answer: 89
Correct? No
Problem: A square plot of land has a perimeter of 132 meters. What is the length of one side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side is 132/4 = <<132/4=33>>33 meters. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. Substituting the given values, we have 138 = 2(46 + W). Solving for W, we get W = (138 - 2*46)/2 = <<(138 - 2*46)/2=49>>49 feet. ### Answer: 49
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. Given that the perimeter is 200 meters and the length is 49 meters, we can substitute these values into the formula to find the width. 200 = 2(49 + W) 100 = 49 + W W = 100 - 49 W = <<100-49=51>>51 meters Therefore, the width of the field is 51 meters. ### Answer: 51
Expected answer: 51
Correct? Yes
Problem: A square has a perimeter of 200m. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 200m / 4 = <<200/4=50>>50m ### Answer: 50m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all four sides. Therefore, 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?
Qwen2-Math 7B:
Reasoning: The length of the fourth side is 207 - (35 + 62 + 70) = <<207-(35+62+70)=30>>30m. ### Answer: 30m
Expected answer: 40
Correct? No
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 384cm and one of the shorter sides (width) is 99cm, we can find the length of the longer sides as follows: 384 = 2(l + 99) 192 = l + 99 l = 192 - 99 l = <<192-99=93>>93cm ### Answer: 93cm
Expected answer: 93
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all four sides. Therefore, the length of the fourth side is 255 - (78 + 15 + 63) = <<255-(78+15+63)=105>>105 m. ### Answer: 105
Expected answer: 99
Correct? No
Problem: A square has a perimeter of 128m. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side is 128/4 = <<128/4=32>>32m. ### Answer: 32m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Given that the perimeter is 96 feet and one pair of opposite sides (the width) is 33 feet, we can set up the equation 96 = 2l + 2(33). Simplifying, we get 96 = 2l + 66, and then 2l = 30. Therefore, the length of the other pair of opposite sides is l = 15 feet. ### Answer: 15 feet
Expected answer: 15
Correct? Yes
Problem: The perimeter of a square field is 112 meters. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of each side is 112/4 = <<112/4=28>>28 meters. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 32 cm / 4 = <<32/4=8>>8 cm The length of one side of the square is 8 cm. ### Answer: 8 cm
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 364m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 364m / 4 = <<364/4=91>>91m ### Answer: 91m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 144 feet and one side (length) is 38 feet, we can set up the equation 144 = 2(38 + w). Solving for w, we get w = (144/2) - 38 = 72 - 38 = <<72-38=34>>34 feet. ### Answer: 34
Expected answer: 34
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of all its sides. We know that two sides add up to 54m and the other two sides add up to 22m and 37m respectively. Therefore, the length of the remaining side can be found by subtracting the sum of the known sides from the total perimeter. Remaining side = Perimeter - (Sum of known sides) Remaining side = 205m - (54m + 22m + 37m) Remaining side = 205m - 113m Remaining side = <<205-113=92>>92m ### Answer: 92m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. Substituting the given values, we have 174 = 2(65 + W). Solving for W, we get W = (174 - 2*65)/2 = <<(174 - 2*65)/2=22>>22m. ### 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?
Qwen2-Math 7B:
Reasoning: 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of each side is 372/4 = <<372/4=93>>93 meters. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where s is the length of one side. Therefore, the length of one side is s = P/4 = <<240/4=60>>60 meters. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that one side (let's assume it's the width) is 97 meters and the perimeter is 242 meters, we can set up the equation 242 = 2(97 + l). Simplifying, we get 242 = 194 + 2l, which leads to 2l = 48, and thus l = 24 meters. Therefore, the length of the other side is 24 meters. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: Tom has constructed a square with a total perimeter of 316 meters. Can you determine the length of each side of this square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where s is the length of one side. Therefore, the length of one side is s = P/4 = <<316/4=79>>79 meters. ### Answer: 79 meters
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 268cm. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 268cm / 4 = <<268/4=67>>67cm Therefore, the length of each side of the square is 67cm. ### Answer: 67cm
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 348m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of each side is 348/4 = <<348/4=87>>87m. ### Answer: 87m
Expected answer: 87
Correct? Yes
Problem: A square has a perimeter of 400m. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 400m / 4 = <<400/4=100>>100m ### Answer: 100m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides. Let's denote the length of the fourth side as x. Then, we have: 81m + 100m + 19m + x = 243m Solving for x, we get: x = 243m - (81m + 100m + 19m) = <<243-(81+100+19)=43>>43m ### Answer: 43m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 186cm and one side (let's assume it's the length) is 50cm, we can set up the equation 186 = 2(50 + w). Solving for w, we get w = (186 - 100) / 2 = 43cm. ### Answer: 43
Expected answer: 43
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 224 cm and the length is 78 cm, we can set up the equation 224 = 2(78 + w). Solving for w, we get w = (224 - 2*78) / 2 = <<(224 - 2*78) / 2=20>>20 cm. ### Answer: 20
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides. We know the lengths of three sides and the total perimeter, so we can find the length of the fourth side by subtracting the sum of the lengths of the three known sides from the total perimeter. The sum of the lengths of the three known sides is 79+97+51 = <<79+97+51=227>>227m. The length of the fourth side is 235-227 = <<235-227=8>>8m. ### Answer: 8m
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 28m / 4 = <<28/4=7>>7m ### Answer: 7m
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 48cm. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 48cm / 4 = <<48/4=12>>12cm ### Answer: 12cm
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side is 184/4 = <<184/4=46>>46 meters. ### Answer: 46
Expected answer: 46
Correct? Yes
Problem: A square has a perimeter of 56 meters. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 56/4 = <<56/4=14>>14 Therefore, the length of each side of the square is 14 meters. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all its sides. Therefore, the length of the fourth side can be found by subtracting the sum of the lengths of the other three sides from the total perimeter. The length of the fourth side is 157 - (97 + 5 + 30) = <<157-(97+5+30)=25>>25m. ### Answer: 25m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all four sides. We know the perimeter is 173m, and the lengths of three sides are 46m, 50m, and 35m. To find the length of the fourth side, we subtract the sum of the lengths of the three known sides from the perimeter. 173 - (46 + 50 + 35) = <<173-(46+50+35)=42>>42m. ### Answer: 42m
Expected answer: 42
Correct? Yes
Problem: A square has a perimeter of 72 cm. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 72 cm / 4 = <<72/4=18>>18 cm ### Answer: 18 cm
Expected answer: 18
Correct? Yes
Problem: A square has a perimeter of 352m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 352m / 4 = <<352/4=88>>88m ### Answer: 88m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. We know that the length L = 23m and the perimeter P = 116m. Substituting these values into the formula, we get 116 = 2(23 + W). Solving for W, we get W = (116 - 2*23)/2 = <<(116 - 2*23)/2=45>>45m. ### Answer: 45m
Expected answer: 35
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 124m / 4 = <<124/4=31>>31m ### Answer: 31m
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?
Qwen2-Math 7B:
Reasoning: The length of the fourth side is 131-(24+57+17) = <<131-(24+57+17)=131-98=33>>33m. ### Answer: 33m
Expected answer: 33
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that one side (let's assume it's the length) is 89m and the perimeter is 254m, we can set up the equation 254 = 2(89 + w). Solving for w, we get w = (254/2) - 89 = <<(254/2)-89=83>>83m. ### Answer: 83m
Expected answer: 38
Correct? No
Problem: A square has a perimeter of 208m. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 208m / 4 = <<208/4=52>>52m ### Answer: 52m
Expected answer: 52
Correct? Yes
Problem: A square has a perimeter of 64m. What is the length of each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 64m / 4 = <<64/4=16>>16m Therefore, the length of each side of the square is 16m. ### Answer: 16m
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?
Qwen2-Math 7B:
Reasoning: The length of the fourth side is 196 - (92 + 29 + 62) = <<196-(92+29+62)=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?
Qwen2-Math 7B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all four sides. Let's denote the length of the fourth side as x. We have the equation: 35 + 76 + 5 + x = 191 Solving for x, we get: x = 191 - (35 + 76 + 5) = <<191-(35+76+5)=75>>75 Therefore, the length of the fourth side is 75 units. ### Answer: 75
Expected answer: 75
Correct? Yes
Problem: A square has a perimeter of 104m. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of each side is 104/4 = <<104/4=26>>26m. ### Answer: 26m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. Substituting the given values, we have 198 = 2(90 + W). Solving for W, we get W = (198/2) - 90 = <<(198/2)-90=54>>54 cm. ### Answer: 54
Expected answer: 9
Correct? No
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Since the perimeter is 128 feet and two sides are 47 feet each, we can set up the equation 128 = 2(47) + 2w. Solving for w, we get w = (128 - 94) / 2 = <<(128-94)/2=17>>17 feet. The length of the remaining two opposite sides should be 17 feet each. ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: A square has a perimeter of 356m. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 356m / 4 = <<356/4=89>>89m ### Answer: 89m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of the quadrilateral is the sum of the lengths of all four sides. Let's denote the length of the fourth side as x. We have the equation: 89 + 87 + 1 + x = 236 Solving for x, we get: x = 236 - 89 - 87 - 1 = <<236-89-87-1=59>>59 Therefore, the length of the fourth side is 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of each side is 340/4 = <<340/4=85>>85 meters. ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: A square has a perimeter of 16m. What is the length of each side?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of each side by dividing the perimeter by 4. 16m / 4 = <<16/4=4>>4m ### Answer: 4m
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?
Qwen2-Math 7B:
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the total perimeter by 4. 316m / 4 = <<316/4=79>>79m ### Answer: 79m
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 300m. How long is each side of the square?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 300m / 4 = <<300/4=75>>75m Each side of the square is 75m long. ### Answer: 75m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all four sides. We can find the length of the remaining side by subtracting the lengths of the other three sides from the perimeter. 198 - 19 - 57 - 22 = <<198-19-57-22=100>>100 The length of the remaining side is 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 172m / 4 = <<172/4=43>>43m ### Answer: 43m
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. Therefore, the length of one side 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Since the shorter sides are 51 meters long, we can substitute w = 51 into the formula. The total perimeter is 158 meters, so we have 158 = 2l + 2(51). Simplifying, we get 158 = 2l + 102. Subtracting 102 from both sides, we get 56 = 2l. Dividing both sides by 2, we get l = 28. Therefore, the length of each of the longer sides is 28 meters. ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: A square has a perimeter of 72m. What is the length of one its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 72m / 4 = <<72/4=18>>18m ### Answer: 18m
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?
Qwen2-Math 7B:
Reasoning: The total length of the fence is 166m, and two opposite sides are 19m each, so the total length of the other two sides is 166 - 2*19 = <<166-2*19=128>>128m. Since the other two sides are equal in length, each side is 128/2 = <<128/2=64>>64m. ### Answer: 64m
Expected answer: 64
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides. We know the lengths of three sides, so we can find the length of the fourth side by subtracting the sum of the lengths of the three known sides from the perimeter. The sum of the lengths of the three known sides is 40m + 32m + 95m = <<40+32+95=167>>167m. The length of the fourth side is 246m - 167m = <<246-167=79>>79m. ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 32m. What is the length of one of its sides?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 32m / 4 = <<32/4=8>>8m ### Answer: 8m
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 12/4 = <<12/4=3>>3 The length of one side of the square is 3 meters. ### 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all four sides. Let's denote the length of the fourth side as x. We can set up the equation: 29 + 16 + 41 + x = 160. Solving for x, we get x = 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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. Given that the perimeter is 98m and one side (let's assume it's the width) is 5m, we can set up the equation 98 = 2(l + 5). Solving for l, we get l = (98 - 10)/2 = <<(98 - 10)/2=44>>44m. ### Answer: 44m
Expected answer: 44
Correct? Yes
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?
Qwen2-Math 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Since the rectangle has two sides measuring 45m each, we can assume that these are the lengths. Therefore, the perimeter can be expressed as P = 2(45) + 2w = 210. Solving for w, we get w = (210 - 2(45)) / 2 = <<(210 - 2(45)) / 2=30>>30m. ### Answer: 30m
Expected answer: 60
Correct? No