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?
Gemini-1.5 Pro:
Reasoning: Let W be the width of the pool. The perimeter of the rectangle is 2 * length + 2 * width, so 324 = 2*83 + 2*W This simplifies to 324 = 166 + 2W Subtracting 166 from both sides gives us 158 = 2W. Dividing both sides by 2 gives us W = 79 meters. ### Answer: 79 meters
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 40m. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of each side is 40/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The length of each side of the square is 344/4 = <<344/4=86>>86 m ### Answer: 86 m
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 348m. What would be the length of each side of the square?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of each side of the square is 348/4 = <<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?
Gemini-1.5 Pro:
Reasoning: Let the length of the other side be 'l' cm. The perimeter of a rectangle is calculated by 2 * (length + width). So, 2 * (49 + l) = 194 cm. This simplifies to 98 + 2l = 194 cm. Further simplifying, 2l = 194 - 98 = 96 cm. Therefore, l = 96 / 2 = 48 cm. ### Answer: 48 cm
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 192m. What is the length of one side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The perimeter is the total length of all the sides added together. Therefore, the length of one side is 192m / 4 = <<192/4=48>>48m. ### Answer: 48m
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of one side is 68/4 = <<68/4=17>>17 cm. ### Answer: 17 cm
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?
Gemini-1.5 Pro:
Reasoning: Let 'l' represent the length and 'w' represent the width of the rectangle. We know l = 4 meters and the perimeter is 52 meters. The perimeter of a rectangle is calculated by the formula: 2*l + 2*w = Perimeter. We can plug in the values we know: 2 * 4 meters + 2 * w = 52 meters. Simplifying, we get 8 meters + 2 * w = 52 meters. Subtracting 8 meters from both sides: 2 * w = 44 meters. Dividing both sides by 2: w = 22 meters. ### Answer: 22 meters
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?
Gemini-1.5 Pro:
Reasoning: The total length of the first three sides of the quadrilateral is 93m + 98m + 36m = <<93+98+36=227>>227m The length of the fourth side is 229m - 227m = <<229-227=2>>2m ### Answer: 2m
Expected answer: 2
Correct? Yes
Problem: The perimeter of a square is 16m. What is the length of each side of this square?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The perimeter is the total length of all the sides added together. Therefore, the length of each side is 16/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The length of each side of the square is 272/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore the length of each side of the square is 244m/4 = 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?
Gemini-1.5 Pro:
Reasoning: The combined length of the three given sides of the quadrilateral is 70m + 29m + 61m = 160m. Therefore, the length of the fourth side is 227m - 160m = 67m. ### Answer: 67m
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 280m. What is the length of the side of that square?
Gemini-1.5 Pro:
Reasoning: A square has four equal sides. The length of one side of the square is 280 / 4 = <<280/4=70>>70 m. ### Answer: 70m
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?
Gemini-1.5 Pro:
Reasoning: The total length of the three known sides is 37cm + 98cm + 41cm = <<37+98+41=176>>176cm. The length of the fourth side is 219cm - 176cm = <<219-176=43>>43cm. ### Answer: 43cm.
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
Gemini-1.5 Pro:
Reasoning: A square has four equal sides. So, we can find the length of one side by dividing the total perimeter by 4: 44 m / 4 = <<44/4=11>>11 m ### Answer: 11 m
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?
Gemini-1.5 Pro:
Reasoning: The two longer sides of the garden measure 71*2 = <<71*2=142>>142 meters. The two shorter sides of the garden measure 282-142 = <<282-142=140>>140 meters. One of the shorter sides measures 140/2 = <<140/2=70>>70 meters. ### Answer: 70 meters
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?
Gemini-1.5 Pro:
Reasoning: The perimeter of a rectangle is twice the sum of its length and width: Perimeter = 2 * (length + width). We know the perimeter is 128 meters and the width is 57 meters. Let the length be represented by 'l'. We can set up an equation: 128 = 2 * (l + 57). Simplify the equation: 128 = 2l + 114. Subtract 114 from both sides: 14 = 2l. Divide both sides by 2 to isolate 'l': l = 7. Therefore, the length of the other side is 7 meters. ### Answer: 7 meters.
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 392m. What is the length of each side of the square?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The length of each side of the square is 392/4 = <<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?
Gemini-1.5 Pro:
Reasoning: Let the length of the other side be 'l'. The perimeter of a rectangle is calculated by 2(l+b), where l is the length and b is the breadth. We know the perimeter is 204m and one side is 16m. So, 2(l + 16) = 204 Simplifying the equation: 2l + 32 = 204 2l = 204 - 32 2l = 172 l = 172/2 = 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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of one side is 336/4 = <<336/4=84>>84cm ### Answer: 84cm
Expected answer: 84
Correct? Yes
Problem: A square has a perimeter of 144 meters. What is the length of one side of the square?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of one side of the square is 144/4 = <<144/4=36>>36 meters. ### Answer: 36 meters
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?
Gemini-1.5 Pro:
Reasoning: The total length of the three sides given is 69+50+39 = <<69+50+39=158>>158 cm. The length of the fourth side is 236-158 = <<236-158=78>>78 cm. ### Answer: 78 cm.
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?
Gemini-1.5 Pro:
Reasoning: The total length of the known sides is 37cm + 14cm + 73cm = <<37+14+73=124>>124cm. So, the length of the unknown side is 193cm - 124cm = <<193-124=69>>69cm. ### Answer: 69cm
Expected answer: 69
Correct? Yes
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The perimeter is the total length of all sides added together. 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?
Gemini-1.5 Pro:
Reasoning: Let W be the width of the rectangle. The perimeter of a rectangle is calculated by 2*(length + width), so 2*(90+W)=228. Dividing both sides of the equation by 2, we get 90+W=114. Then, subtracting 90 from both sides, we obtain W=24. ### Answer: 24 meters.
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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of one side of the field is 136/4 = <<136/4=34>>34 meters. ### Answer: 34 meters
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?
Gemini-1.5 Pro:
Reasoning: The opposite sides of a rectangle are equal in length. ### Answer: 43 meters
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?
Gemini-1.5 Pro:
Reasoning: The perimeter is the sum of the length of all the sides of the quadrilateral. The length of three of the sides is 58m + 54m + 1m = 113m. The length of the missing portion is 206m - 113m = 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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, each side of this square field is 284/4 = <<284/4=71>>71 meters long. ### Answer: 71 meters
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?
Gemini-1.5 Pro:
Reasoning: Let W be the width of the rectangle. The perimeter of a rectangle is calculated as 2 * (length + width). We know the perimeter is 150 feet and the length is 69 feet. So, 150 = 2 * (69 + W) Simplifying, 150 = 138 + 2W Subtracting 138 from both sides, we get 12 = 2W Dividing both sides by 2, we get W = 6 feet. ### Answer: 6 feet
Expected answer: 6
Correct? Yes
Problem: The perimeter of a rectangle is 166m. If one of the sides measures 35m, how long is the other side?
Gemini-1.5 Pro:
Reasoning: * The perimeter of a rectangle is twice the sum of its length and width: Perimeter = 2 * (length + width) * We know the perimeter is 166m and one side (let's say the width) is 35m. Let the unknown side (the length) be represented by 'l'. We can plug these values into the formula: 166 = 2 * (l + 35) * Simplifying the equation: 166 = 2l + 70 * Subtracting 70 from both sides: 96 = 2l * Dividing both sides by 2 to isolate 'l': l = 48 ### Answer: 48m
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has four equal sides. So, the length of each side is 124/4 = <<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?
Gemini-1.5 Pro:
Reasoning: Since it's a rectangle, opposite sides have the same length, so the opposite side is also 79 feet long. ### Answer: 79 feet.
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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of one side of the square is 132 meters / 4 = <<132/4=33>>33 meters. ### Answer: 33 meters
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?
Gemini-1.5 Pro:
Reasoning: Let 'w' represent the width of the rectangle. The perimeter of a rectangle is calculated by the formula: Perimeter = 2 * (length + width) We know the perimeter is 138 feet and the length is 46 feet. Let's plug these values into the formula: 138 = 2 * (46 + w) Simplifying the equation: 138 = 92 + 2w Subtracting 92 from both sides: 138 - 92 = 2w This simplifies to: 46 = 2w Dividing both sides by 2 to isolate 'w': 46 / 2 = w Therefore, the width (w) is 23 feet. ### Answer: 23 feet
Expected answer: 23
Correct? Yes
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?
Gemini-1.5 Pro:
Reasoning: The perimeter of a rectangle is calculated by the formula: Perimeter = 2 * (Length + Width). We can rearrange this formula to solve for the width: Width = (Perimeter / 2) - Length. In this case: Width = (200 meters / 2) - 49 meters = 100 meters - 49 meters = 51 meters. ### Answer: 51 meters.
Expected answer: 51
Correct? Yes
Problem: A square has a perimeter of 200m. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of each side is 200/4 = <<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?
Gemini-1.5 Pro:
Reasoning: The total length of the first three sides is 9+30+71 = <<9+30+71=110>>110m. Thus, the length of the fourth side is 199-110 = <<199-110=89>>89m. ### Answer: 89m
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?
Gemini-1.5 Pro:
Reasoning: The total length of the three sides is 35+62+70 = <<35+62+70=167>>167m The length of the fourth side is 207-167 = <<207-167=40>>40m ### Answer: 40m
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?
Gemini-1.5 Pro:
Reasoning: Let the length of the longer side be L. The perimeter of a rectangle is calculated as 2*(length + width). We are told the perimeter is 384cm and the shorter side is 99cm. We can therefore write the equation 384 = 2 * (L + 99). Solving for L: * 192 = L + 99 * 192 - 99 = L * 93 = L Therefore, the length of the longer side is 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?
Gemini-1.5 Pro:
Reasoning: The total length of the first three sides of the quadrilateral is 78+15+63 = <<78+15+63=156>>156 m The length of the fourth side is 255-156 = <<255-156=99>>99 m ### Answer: 99 m
Expected answer: 99
Correct? Yes
Problem: A square has a perimeter of 128m. What is the length of one of its sides?
Gemini-1.5 Pro:
Reasoning: A square has four equal sides. The perimeter is the total length of all the sides added together. Therefore, the length of one side of the square is 128m / 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?
Gemini-1.5 Pro:
Reasoning: Since a rectangle has two pairs of equal opposite sides, the total length of the known sides is 33*2 = <<33*2=66>>66 feet. The total length of the other two sides of the rectangle is 96-66 = <<96-66=30>>30 feet. Since the other two sides are opposite and equal in length, each side is 30/2 = <<30/2=15>>15 feet long. ### 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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The length of each side is 112/4 = <<112/4=28>>28 meters. ### Answer: 28 meters
Expected answer: 28
Correct? Yes
Problem: The perimeter of a square is 32 cm. Can you find the length of one of its sides?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The perimeter is the total length of all the sides added together. Therefore, the length of one side of the square is 32 cm / 4 = <<32/4=8>>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?
Gemini-1.5 Pro:
Reasoning: A square has four equal sides. We can find the length of one side by dividing the total perimeter by 4. So, each side of the square is 364m / 4 = <<364/4=91>>91m long. ### 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?
Gemini-1.5 Pro:
Reasoning: The perimeter of a rectangle is twice the sum of its length and width. We know the perimeter is 144 feet and the length is 38 feet. Let the unknown width be 'w'. We can set up the equation: 2 * (38 + w) = 144 Simplifying, we get: 76 + 2w = 144 Subtracting 76 from both sides: 2w = 68 Dividing both sides by 2: w = 34 feet ### Answer: 34 feet
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?
Gemini-1.5 Pro:
Reasoning: The total length of the three sides given is 54m + 22m + 37m = <<54+22+37=113>>113m. The length of the remaining side is 205m - 113m = <<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?
Gemini-1.5 Pro:
Reasoning: Let the width of the field be w. The perimeter of a rectangle is calculated as: 2(length + width) Therefore, we can set up the following equation: 2(65 + w) = 174 Expanding the equation, we get: 130 + 2w = 174 Combining like terms, we get: 2w = 44 Solving for w, we get: w = 22m ### Answer: 22m
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?
Gemini-1.5 Pro:
Reasoning: The combined length of the three sides is 25+17+89 = <<25+17+89=131>>131 cm The length of the fourth side is 176-131 = <<176-131=45>>45 cm. ### Answer: 45 cm.
Expected answer: 45
Correct? Yes
Problem: A square has a perimeter of 372 meters. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has four equal sides. The perimeter is the total length of all the sides added together. So, the length of each side is 372/4 = <<372/4=93>>93 meters. ### Answer: 93 meters
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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The perimeter is the total length of all sides added together. Therefore, the length of one side of the square field is 240 meters / 4 sides = 60 meters. ### Answer: 60 meters.
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?
Gemini-1.5 Pro:
Reasoning: Let's denote the unknown side length as 'l'. The perimeter of a rectangle is calculated by adding the lengths of all its sides: 2 * length + 2 * width = perimeter. We know the perimeter is 242 meters and one side is 97 meters. Let's plug these values into the formula: 2 * 97 + 2 * l = 242 Simplifying the equation: 194 + 2l = 242 To isolate 'l', subtract 194 from both sides: 2l = 48 Finally, divide both sides by 2 to find the length of the other side: l = 24 meters ### Answer: 24 meters
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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of each side is the total perimeter divided by 4. So, each side of the square is 316 meters / 4 = <<316/4=79>>79 meters long. ### 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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of each side is 268/4 = <<268/4=67>>67 cm. ### Answer: 67 cm
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 348m. What is the length of each side of the square?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. 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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of one side is 400/4 = <<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?
Gemini-1.5 Pro:
Reasoning: The perimeter of a quadrilateral is the sum of its four sides. Let the fourth side have length $x$ meters. We have the equation $x + 81 + 100 + 19 = 243$. Combining terms on the left side, we have $x+200 = 243$. Subtracting $200$ from both sides gives $x=43$. ### 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?
Gemini-1.5 Pro:
Reasoning: The perimeter of a rectangle is calculated by adding up the lengths of all four sides. Since two sides of the rectangle are the same length, we can calculate the total length of two sides by the following calculation: 186 cm / 2 = 93 cm. We also know one side is 50 cm long. That means the other side has to be 93 cm - 50 cm = 43 cm long. ### Answer: 43 cm
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?
Gemini-1.5 Pro:
Reasoning: Let the length of the adjacent side be 'x' cm. The perimeter of a rectangle is calculated by 2 * (length + width). So, 2 * (78 + x) = 224 Simplifying the equation: 156 + 2x = 224 2x = 224 - 156 2x = 68 x = 68/2 = 34 Therefore, the length of the adjacent side is 34 cm. ### Answer: 34 cm
Expected answer: 34
Correct? Yes
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?
Gemini-1.5 Pro:
Reasoning: The combined length of the three known sides of the quadrilateral is 79m + 97m + 51m = <<79+97+51=227>>227m. The length of the fourth side is 235m - 227m = <<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?
Gemini-1.5 Pro:
Reasoning: A square has four equal sides. Therefore, the length of one side of the square = 28/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The length of each side is 48/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of one side of the square plot of land is 184/4 = <<184/4=46>>46 meters. ### Answer: 46 meters
Expected answer: 46
Correct? Yes
Problem: A square has a perimeter of 56 meters. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has 4 sides that are equal in length. The length of each side of the square is 56/4 = <<56/4=14>>14 meters. ### Answer: 14 meters
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?
Gemini-1.5 Pro:
Reasoning: The total length of the three given sides is 97m + 5m + 30m = 132m. The length of the fourth side is 157m - 132m = 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?
Gemini-1.5 Pro:
Reasoning: The total length of the first three sides is 46m + 50m + 35m = <<46+50+35=131>>131m The length of the fourth side is 173m - 131m = <<173-131=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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The length of one side is 72 / 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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of each side of the square is 352/4 = <<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?
Gemini-1.5 Pro:
Reasoning: The perimeter of a rectangle is calculated with the following formula: Perimeter = 2 * (Length + Width). We know the perimeter is 116m and the length is 23m so 116 = 2 * (23 + Width). Dividing both sides of the equation by 2 gives us 58 = 23 + Width. Finally, we can solve for the width: Width = 58 - 23 = 35m. ### Answer: 35m
Expected answer: 35
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of each side is 124/4 = <<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?
Gemini-1.5 Pro:
Reasoning: The total length of the three given sides is 24m + 57m + 17m = <<24+57+17=98>>98m The length of the fourth side is 131m - 98m = <<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?
Gemini-1.5 Pro:
Reasoning: The two sides of the rectangle with length 89m put together have a length of 89*2 = <<89*2=178>>178m. The two other sides of the rectangle therefore have a combined length of 254-178 = <<254-178=76>>76m. Since both sides are the same length, the other side has a length of 76/2 = <<76/2=38>>38m. ### Answer: 38m
Expected answer: 38
Correct? Yes
Problem: A square has a perimeter of 208m. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of each side is 208/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of each side of the square is 64/4 = <<64/4=16>>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?
Gemini-1.5 Pro:
Reasoning: To find the length of the fourth side, we subtract the combined length of the three sides from the total perimeter: 196 meters - 183 meters = 13 meters. ### Answer: 13 meters.
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?
Gemini-1.5 Pro:
Reasoning: The total length of the three given sides of the quadrilateral is 35+76+5 = <<35+76+5=116>>116 units. The length of the fourth side is the total perimeter minus the length of the other three sides, or 191-116 = <<191-116=75>>75 units. ### Answer: 75 units.
Expected answer: 75
Correct? Yes
Problem: A square has a perimeter of 104m. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, 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?
Gemini-1.5 Pro:
Reasoning: The perimeter of a rectangle is calculated by the formula: Perimeter = 2 * (Length + Width). We know the perimeter is 198 cm and the length is 90 cm. Let's substitute these values into the formula and solve for the width: 198 cm = 2 * (90 cm + Width) 198 cm = 180 cm + 2 * Width 18 cm = 2 * Width Width = 18 cm / 2 = 9 cm ### Answer: 9 cm
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?
Gemini-1.5 Pro:
Reasoning: The two sides that are 47 feet each sum up to 47*2 = <<47*2=94>>94 feet. That leaves 128-94 = <<128-94=34>>34 feet of perimeter for the other two sides. Since the other two sides are opposite sides of a rectangle, they must be equal in length, meaning each of the remaining sides should be 34/2 = <<34/2=17>>17 feet long. ### Answer: 17 feet
Expected answer: 17
Correct? Yes
Problem: A square has a perimeter of 356m. What is the length of one of its sides?
Gemini-1.5 Pro:
Reasoning: The perimeter of a square is calculated by multiplying the length of one side by 4. Therefore, to find the length of one side, we can divide the perimeter by 4. The length of one side of this square is 356/4 = <<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?
Gemini-1.5 Pro:
Reasoning: The total length of the first three sides of the quadrilateral is 89+87+1 = <<89+87+1=177>>177 units. Thus, the length of the fourth side is 236-177 = <<236-177=59>>59 units. ### Answer: 59 units.
Expected answer: 59
Correct? Yes
Problem: A square has a perimeter of 340 meters. What is the length of each side of this square?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of each side of the square is 340/4 = <<340/4=85>>85 meters. ### Answer: 85 meters
Expected answer: 85
Correct? Yes
Problem: A square has a perimeter of 16m. What is the length of each side?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of each side is 16/4 = <<16/4=4>>4 meters. ### Answer: 4 meters
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?
Gemini-1.5 Pro:
Reasoning: The total length of the first three sides of the quadrilateral is 1 + 54 + 9 = 64m The length of the fourth side is 81 - 64 = 17m ### Answer: 17m
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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. So, the length of each side of the square is 316/4 = <<316/4=79>>79 m. ### Answer: 79 m
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 300m. How long is each side of the square?
Gemini-1.5 Pro:
Reasoning: A square has 4 sides of equal length. Therefore, the side length of the square is 300/4 = <<300/4=75>>75m. ### 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?
Gemini-1.5 Pro:
Reasoning: The combined length of the three sides is 19+57+22 = <<19+57+22=98>>98m The length of the remaining side is 198-98 = <<198-98=100>>100m ### Answer: 100m
Expected answer: 100
Correct? Yes
Problem: A square has a perimeter of 172m. What is the length of each side of the square?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of each side of the square is 172/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of one side is 304/4 = <<304/4=76>>76 cm. ### Answer: 76 cm
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?
Gemini-1.5 Pro:
Reasoning: The two shorter sides of the rectangle combine to be 51*2 = <<51*2=102>>102 meters long. That means the two longer sides combine to be 158-102 = <<158-102=56>>56 meters long. Since the two longer sides are of equal length, each longer side is 56/2 = <<56/2=28>>28 meters long. ### Answer: 28 meters
Expected answer: 28
Correct? Yes
Problem: A square has a perimeter of 72m. What is the length of one its sides?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The length of one side is 72/4 = <<72/4=18>>18 m. ### Answer: 18 m
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?
Gemini-1.5 Pro:
Reasoning: The two opposite sides of 19m each add up to 19*2 = <<19*2=38>>38m. The other two sides of the fence account for 166-38 = <<166-38=128>>128m of fencing. Since the last two sides are opposite and equal in length, each side is 128/2 = <<128/2=64>>64m long. ### 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?
Gemini-1.5 Pro:
Reasoning: The total length of the three sides of the quadrilateral is 40+32+95 = <<40+32+95=167>>167 m. The length of the fourth side is 246-167 = <<246-167=79>>79 m. ### Answer: 79 m
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 32m. What is the length of one of its sides?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. Therefore, the length of one side is 32/4 = <<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?
Gemini-1.5 Pro:
Reasoning: A square has 4 equal sides. The perimeter is the total length of all the sides added together. Therefore, the length of one side of the square is 12 meters / 4 sides = 3 meters/side. ### Answer: 3 meters
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?
Gemini-1.5 Pro:
Reasoning: The total length of the three known sides of the quadrilateral is 29m + 16m + 41m = 86m. The length of the fourth side is 160m - 86m = 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?
Gemini-1.5 Pro:
Reasoning: Let the length of the other side be *l* meters. The perimeter of a rectangle is calculated by 2 * (length + width). We know the perimeter is 98m and one side is 5m. We can set up the equation: 2 * (5 + *l*) = 98 Simplifying the equation: 10 + 2*l* = 98 Solving for *l*: 2*l* = 88 Therefore, *l* = 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?
Gemini-1.5 Pro:
Reasoning: The two sides of the rectangle with the known measurement give us 45*2 = <<45*2=90>>90m of the perimeter. This leaves 210-90 = <<210-90=120>>120m of the perimeter for the other two sides. Since the other two sides are equal in length, each of the other two sides is 120/2 = <<120/2=60>>60m. ### Answer: 60m
Expected answer: 60
Correct? Yes