Claude-3 Sonnet 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangular swimming pool is 324 meters. - The length of the pool is 83 meters. Let's denote the width of the pool as w. Perimeter = 2 × (length + width) 324 = 2 × (83 + w) 324 = 166 + 2w 158 = 2w w = 79 meters Therefore, the width of the pool is 79 meters. ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 40m. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 40 meters. Step 1: Set up the equation using the given information. 40 = 4 × side length Step 2: Solve for the side length by dividing both sides by 4. side length = 40 / 4 side length = 10 meters Therefore, the length of each side of the square is 10 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 344 meters. Step 1: Define the perimeter of a square. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Perimeter = 4 × side length Step 2: Set up an equation using the given information. 344 meters = 4 × side length Step 3: Solve for the side length. Side length = 344 meters / 4 Side length = 86 meters Therefore, the length of each side of the square is 86 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The shape is a square. - The perimeter of the square is 348 meters. Step 1: Define the perimeter of a square. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Perimeter = 4 × side length Step 2: Set up an equation using the given information. 348 meters = 4 × side length Step 3: Solve for the side length. Side length = 348 meters / 4 Side length = 87 meters Therefore, the length of each side of the square with a perimeter of 348 meters is 87 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is given by: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 194 cm. - The length of one side is 49 cm. Let's denote the length of the other side as x. Perimeter = 2 × (length + width) 194 = 2 × (49 + x) 194 = 98 + 2x 2x = 194 - 98 2x = 96 x = 96/2 x = 48 Therefore, the length of the other side of the rectangle is 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?
Claude-3 Sonnet:
To solve this problem, we need to find the relationship between the perimeter of a square and the length of its sides. Given information: - The shape is a square. - The perimeter of the square is 192 meters. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Let's represent the length of one side as x. Perimeter of a square = 4 × length of one side 192 meters = 4x Dividing both sides by 4, we get: x = 192 meters / 4 x = 48 meters Therefore, the length of one side of the square is 48 meters. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 68 cm. Step 1: Set up the equation using the given information. 68 cm = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 68 cm / 4 side length = 17 cm Therefore, the length of one side of the square is 17 cm. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 52 meters. - One of the sides (let's call it the width) is 4 meters. Let's denote the other side (length) as x. Substituting the given values into the perimeter formula, we get: 52 = 2 × (x + 4) 52 = 2x + 8 44 = 2x x = 22 Therefore, the length of the other side is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 229 meters. - Two sides have lengths of 93 meters and 98 meters, respectively. - The third side has a length of 36 meters. Let's denote the length of the fourth side as x. Perimeter of the quadrilateral = Sum of the lengths of all four sides 229 = 93 + 98 + 36 + x Rearranging the terms, we get: x = 229 - 93 - 98 - 36 x = 2 Therefore, the length of the fourth side of the quadrilateral is 2 meters. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: The perimeter of a square is 16m. What is the length of each side of this square?
Claude-3 Sonnet:
To solve this problem, we need to find the relationship between the perimeter of a square and the length of its sides. Given information: - The perimeter of the square is 16 meters. The perimeter of a square is the total distance around the square, which is the sum of the lengths of all four sides. Let's represent the length of one side as x. Perimeter of a square = 4 × length of one side 16 meters = 4x Dividing both sides by 4, we get: x = 16 meters / 4 x = 4 meters Therefore, the length of each side of the square is 4 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 272 meters. Step 1: Define the perimeter of a square in terms of its side length. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the equation and solve for the side length. 272 meters = 4 × side length side length = 272 meters / 4 side length = 68 meters Therefore, the length of each side of the square is 68 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 244 meters. Step 1: Define the perimeter of a square. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Perimeter = 4 × side length Step 2: Set up an equation using the given information. 244 meters = 4 × side length Step 3: Solve for the side length. Side length = 244 meters / 4 Side length = 61 meters Therefore, the length of each side of the square is 61 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 227 meters. - The lengths of three sides are 70 meters, 29 meters, and 61 meters. Let's represent the unknown length of the fourth side as x. Perimeter of the quadrilateral = Sum of the lengths of all four sides 227 = 70 + 29 + 61 + x Rearranging the terms, we get: 227 - 70 - 29 - 61 = x 227 - 160 = x x = 67 meters Therefore, the length of the fourth side of the quadrilateral is 67 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 280 meters. Step 1: Set up the equation using the given information. 280 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 280 / 4 side length = 70 meters Therefore, the length of the side of the square with a perimeter of 280 meters is 70 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 219 cm. - Two sides have lengths of 37 cm and 98 cm. - One side has a length of 41 cm. Let's represent the unknown length of the fourth side as x. Perimeter = Sum of all four sides 219 cm = 37 cm + 98 cm + 41 cm + x Rearranging the terms, we get: 219 cm - 37 cm - 98 cm - 41 cm = x 43 cm = x Therefore, the length of the fourth side of the quadrilateral is 43 cm. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 44 meters. Step 1: Set up the equation using the given information. 44 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 44 / 4 side length = 11 meters Therefore, the length of one side of the square is 11 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle: P = 2(l + w), where P is the perimeter, l is the length, and w is the width. Given information: - The perimeter of the rectangular garden is 282 meters. - The longer side measures 71 meters. Let's denote the shorter side as w. Step 1: Substitute the given values into the perimeter formula. 282 = 2(71 + w) Step 2: Simplify the equation. 282 = 142 + 2w Step 3: Subtract 142 from both sides. 282 - 142 = 2w 140 = 2w Step 4: Divide both sides by 2 to find the value of w. 140/2 = w w = 70 meters Therefore, the length of the shorter side of the rectangular garden is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The total perimeter of the rectangular garden is 128 meters. - The shorter side of the garden has a length of 57 meters. Let's denote the longer side of the garden as x. Perimeter = 2 × (length + width) 128 = 2 × (57 + x) 128 = 114 + 2x 14 = 2x 7 = x Therefore, the longer side of the garden has a length of 7 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 392 meters. Step 1: Define the perimeter of a square in terms of its side length. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the equation and solve for the side length. 392 meters = 4 × side length side length = 392 meters / 4 side length = 98 meters Therefore, the length of each side of the square is 98 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 204 meters. - One of the sides (let's call it the length) is 16 meters. Let's denote the other side (the width) as w. Perimeter = 2 × (length + width) 204 = 2 × (16 + w) 204 = 32 + 2w 172 = 2w w = 86 meters Therefore, the length of the other side (the width) is 86 meters. ### Answer: 86
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 336cm. What is the length of one of its sides?
Claude-3 Sonnet:
To solve this problem, we need to find the relationship between the perimeter of a square and the length of its sides. Given information: - The shape is a square. - The perimeter of the square is 336 cm. Step 1: Find the formula for the perimeter of a square. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the formula and solve for the side length. 336 cm = 4 × side length Side length = 336 cm / 4 Side length = 84 cm Therefore, the length of one side of the square is 84 cm. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 144 meters. Step 1: Set up the equation using the given information. 144 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 144 / 4 side length = 36 meters Therefore, 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 236 cm. - Two sides measure 69 cm and 50 cm, respectively. - A third side measures 39 cm. Let's represent the length of the fourth side as x. Perimeter = Sum of all four sides 236 cm = 69 cm + 50 cm + 39 cm + x Simplifying the equation: 236 cm = 158 cm + x x = 236 cm - 158 cm x = 78 cm Therefore, the length of the fourth side of the quadrilateral 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 193 cm. - Two sides measure 37 cm and 14 cm. - One side measures 73 cm. - One side has an unknown length, which we need to find. Let's call the unknown length x. Step 1: Write the equation for the perimeter. Perimeter = 37 cm + 14 cm + 73 cm + x Step 2: Substitute the given perimeter value and solve for x. 193 cm = 37 cm + 14 cm + 73 cm + x 193 cm = 124 cm + x x = 193 cm - 124 cm x = 69 cm Therefore, the length of the unknown side of the quadrilateral is 69 cm. ### Answer: 69
Expected answer: 69
Correct? Yes
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 160 meters. Step 1: Set up the equation using the given information. 160 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 160 / 4 side length = 40 meters Therefore, the length of one side of the square is 40 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 228 meters. - The length of the rectangle is 90 meters. Step 1: Substitute the known values into the perimeter formula. 228 = 2 × (90 + width) Step 2: Simplify the equation. 228 = 180 + 2 × width Step 3: Subtract 180 from both sides of the equation. 48 = 2 × width Step 4: Divide both sides of the equation by 2 to find the width. width = 48 / 2 width = 24 meters Therefore, the width of the rectangle is 24 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square field given its perimeter. Given information: - The perimeter of the square field is 136 meters. - In a square, all sides are equal. The perimeter of a square is the sum of the lengths of all four sides. Let the length of one side be x meters. Perimeter of the square = 4 × x (since all sides are equal) We know that the perimeter is 136 meters, so we can set up an equation: 4 × x = 136 Solving for x: x = 136 / 4 x = 34 Therefore, the length of one side of the square field is 34 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is given by: Perimeter = 2 × (length + width) Given information: - The total perimeter of the rectangle is 236 meters. - One side of the rectangle is 43 meters. Let's denote the length of the opposite side as x. Step 1: Set up the equation using the perimeter formula. 236 = 2 × (43 + x) Step 2: Simplify the equation. 236 = 86 + 2x Step 3: Subtract 86 from both sides. 236 - 86 = 2x 150 = 2x Step 4: Divide both sides by 2 to find x. x = 150 / 2 x = 75 Therefore, the length of the opposite side of the rectangle 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?
Claude-3 Sonnet:
To solve this problem, we need to find the sum of the lengths of the given sides and then subtract it from the total perimeter to find the length of the missing portion. Given information: - The perimeter of the quadrilateral is 206 meters. - Two sides together have a length of 58 meters. - The other two sides have lengths of 54 meters and 1 meter, respectively. Step 1: Find the sum of the lengths of the given sides. Sum of the given sides = 58 meters + 54 meters + 1 meter Sum of the given sides = 113 meters Step 2: Find the length of the missing portion of the perimeter. Length of the missing portion = Total perimeter - Sum of the given sides Length of the missing portion = 206 meters - 113 meters Length of the missing portion = 93 meters Therefore, the length of the missing portion of the perimeter is 93 meters. ### Answer: 93
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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square field given its total perimeter. Given information: - The field is a square. - The total perimeter of the square field is 284 meters. Step 1: Define the variable. Let x be the length of one side of the square field. Step 2: Write an equation for the perimeter of the square. Perimeter of a square = 4 × length of one side 284 = 4x Step 3: Solve the equation for x. 284 = 4x x = 284 / 4 x = 71 Therefore, each side of the square field is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is given by: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 150 feet. - The length of the rectangle is 69 feet. Step 1: Substitute the known values into the perimeter formula. 150 = 2 × (69 + width) Step 2: Simplify the equation. 150 = 138 + 2 × width Step 3: Subtract 138 from both sides of the equation. 12 = 2 × width Step 4: Divide both sides of the equation by 2 to find the width. width = 12 / 2 width = 6 feet Therefore, the width of the rectangle is 6 feet. ### Answer: 6
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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 166 meters. - One of the sides (let's call it the width) measures 35 meters. Let's denote the other side (length) as x. Substituting the given values into the perimeter formula, we get: 166 = 2 × (x + 35) 166 = 2x + 70 96 = 2x x = 48 meters Therefore, the length of the other side of the rectangle is 48 meters. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The shape is a square. - The perimeter of the square is 124 meters. Step 1: Define the perimeter of a square. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Perimeter = 4 × side length Step 2: Set up an equation using the given information. Perimeter = 4 × side length 124 meters = 4 × side length Step 3: Solve for the side length. side length = 124 meters / 4 side length = 31 meters Therefore, the length of each side of the square is 31 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle: Perimeter = 2 × (length + width). Given information: - The perimeter of the rectangular field is 336 feet. - The length of one side is 79 feet. Let's denote the length of the opposite side as x. Step 1: Write the equation for the perimeter using the given information. Perimeter = 2 × (79 + x) 336 = 2 × (79 + x) Step 2: Solve the equation for x. 336 = 158 + 2x 178 = 2x x = 89 feet Therefore, the length of the opposite side of the rectangular field 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?
Claude-3 Sonnet:
To solve this problem, we need to find the relationship between the perimeter of a square and the length of its sides. Given information: - The plot of land is a square. - The perimeter of the square is 132 meters. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Let's represent the length of one side as x. Perimeter of a square = 4 × length of one side 132 meters = 4x Dividing both sides by 4, we get: x = 132 / 4 x = 33 meters Therefore, the length of one side of the square plot of land is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 138 feet. - The length of the rectangle is 46 feet. Step 1: Substitute the known values into the perimeter formula. 138 = 2 × (46 + width) Step 2: Simplify the equation. 138 = 92 + 2 × width Step 3: Subtract 92 from both sides of the equation. 138 - 92 = 2 × width 46 = 2 × width Step 4: Divide both sides of the equation by 2 to find the width. width = 46 / 2 width = 23 feet Therefore, the width of the rectangle is 23 feet. ### Answer: 23
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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The total perimeter of the rectangular field is 200 meters. - The length of the field is 49 meters. Let's denote the width of the field as w. Perimeter = 2 × (length + width) 200 = 2 × (49 + w) 200 = 98 + 2w 102 = 2w w = 102 / 2 w = 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 200 meters. Step 1: Set up the equation using the given information. 200 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 200 / 4 side length = 50 meters Therefore, the length of each side of the square is 50 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 199 meters. - The length of one side is 9 meters. - The length of the second side is 30 meters. - The length of the third side is 71 meters. Let's represent the length of the fourth side as x. Perimeter = Sum of the lengths of all four sides 199 = 9 + 30 + 71 + x Rearranging the terms, we get: x = 199 - (9 + 30 + 71) x = 199 - 110 x = 89 Therefore, the length of the fourth side of the quadrilateral is 89 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 207 meters. - The lengths of three sides are 35 meters, 62 meters, and 70 meters. Let's represent the length of the fourth side as x. Perimeter = Sum of all four sides 207 = 35 + 62 + 70 + x Rearranging the terms, we get: x = 207 - (35 + 62 + 70) x = 207 - 167 x = 40 meters Therefore, the length of the fourth side of the quadrilateral is 40 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is given by: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 384 cm. - One of the shorter sides (width) is 99 cm. Let's denote the length of the longer side as x. Step 1: Set up the equation using the perimeter formula. Perimeter = 2 × (length + width) 384 = 2 × (x + 99) Step 2: Solve for x. 384 = 2x + 198 2x = 384 - 198 2x = 186 x = 186 / 2 x = 93 Therefore, the length of the longer sides of the rectangle is 93 cm. ### Answer: 93
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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 255 m. - The length of the first side is 78 m. - The length of the second side is 15 m. - The length of the third side is 63 m. Let's denote the length of the fourth side as x. Perimeter = Sum of the lengths of all four sides 255 m = 78 m + 15 m + 63 m + x Rearranging the terms, we get: x = 255 m - 78 m - 15 m - 63 m x = 255 m - 156 m x = 99 m Therefore, the length of the fourth side of the quadrilateral is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 128 meters. Step 1: Set up the equation using the given information. 128 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 128 / 4 side length = 32 meters Therefore, the length of one side of the square is 32 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is given by: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 96 feet. - One pair of opposite sides (let's call them the length) is 33 feet each. Let's denote the other pair of opposite sides (the width) as x. Perimeter = 2 × (length + width) 96 = 2 × (33 + x) 96 = 66 + 2x 2x = 96 - 66 2x = 30 x = 15 Therefore, the length of the other pair of opposite sides (the width) is 15 feet. ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: The perimeter of a square field is 112 meters. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to find the relationship between the perimeter of a square and its side length, and then use the given perimeter to calculate the side length. Given information: - The shape is a square. - The perimeter of the square is 112 meters. Step 1: Find the formula for the perimeter of a square. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the formula and solve for the side length. 112 meters = 4 × side length Side length = 112 meters / 4 Side length = 28 meters Therefore, the length of each side of the square field is 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?
Claude-3 Sonnet:
To find the length of one side of a square, given its perimeter, we can use the following steps: 1. The perimeter of a square is the total distance around the square, which is the sum of the lengths of all four sides. 2. Since all sides of a square are equal, we can represent the length of one side as x. 3. The perimeter formula for a square is: Perimeter = 4 × (length of one side) 4. Substituting the given perimeter of 32 cm, we get: 32 = 4x 5. Dividing both sides by 4, we get: x = 32/4 = 8 Therefore, the length of one side of the square with a perimeter of 32 cm 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 364 meters. Step 1: Write the formula for the perimeter of a square. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the formula and solve for the side length. 364 meters = 4 × side length side length = 364 meters / 4 side length = 91 meters Therefore, the length of each side of the square is 91 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The total perimeter of the rectangle is 144 feet. - The length of one side is 38 feet. Let's denote the length of the other side as x. Perimeter = 2 × (length + width) 144 = 2 × (38 + x) 144 = 76 + 2x 2x = 144 - 76 2x = 68 x = 34 Therefore, the length of the other side of the rectangle is 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?
Claude-3 Sonnet:
To solve this problem, we need to find the sum of the given side lengths and then subtract it from the total perimeter to find the length of the remaining side. Given information: - The perimeter of the quadrilateral is 205 meters. - Two sides add up to 54 meters. - Two other sides add up to 22 meters and 37 meters, respectively. Step 1: Find the sum of the given side lengths. Sum of the given side lengths = 54 + 22 + 37 = 113 meters Step 2: Find the length of the remaining side by subtracting the sum of the given side lengths from the total perimeter. Length of the remaining side = Total perimeter - Sum of the given side lengths Length of the remaining side = 205 - 113 = 92 meters Therefore, the length of the remaining side to complete the perimeter of the quadrilateral is 92 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangular field is 174 meters. - The length of the field is 65 meters. Let's denote the width of the field as w. Perimeter = 2 × (length + width) 174 = 2 × (65 + w) 174 = 130 + 2w 44 = 2w w = 22 meters Therefore, the width of the field is 22 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the property that the sum of the lengths of all sides of a quadrilateral is equal to its perimeter. Given information: - The perimeter of the quadrilateral is 176 cm. - The lengths of three sides are 25 cm, 17 cm, and 89 cm. Let's denote the length of the fourth side as x. Step 1: Set up an equation using the perimeter formula. Perimeter = Sum of all side lengths 176 cm = 25 cm + 17 cm + 89 cm + x Step 2: Solve for x by rearranging the equation. 176 cm = 131 cm + x x = 176 cm - 131 cm x = 45 cm Therefore, the length of the fourth side of the quadrilateral is 45 cm. ### Answer: 45
Expected answer: 45
Correct? Yes
Problem: A square has a perimeter of 372 meters. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The shape is a square. - The perimeter of the square is 372 meters. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Let's represent the length of one side as x. Perimeter of a square = 4 × length of one side 372 meters = 4x Dividing both sides by 4, we get: x = 372 / 4 x = 93 meters Therefore, the length of each side of the square is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square field is 240 meters. Step 1: Set up the equation using the given information. 240 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 240 / 4 side length = 60 meters Therefore, the length of one side of the square field is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 242 meters. - One of the sides (let's assume it's the length) is 97 meters. Let's denote the unknown side (width) as w. Perimeter = 2 × (length + width) 242 = 2 × (97 + w) 242 = 194 + 2w 48 = 2w w = 24 meters Therefore, the length of the other side (width) of the rectangle is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is given by: Perimeter = 4 × side length Given information: - The total perimeter of the square is 316 meters. Step 1: Set up the equation using the given information. Perimeter = 4 × side length 316 = 4 × side length Step 2: Solve for the side length. 316 = 4 × side length side length = 316 / 4 side length = 79 meters Therefore, the length of each side of the square is 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 268 cm. Step 1: Define the perimeter of a square. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Let's represent the length of one side as x. Perimeter of a square = 4 × x Step 2: Substitute the given perimeter value into the equation. 268 cm = 4 × x Step 3: Solve for x by dividing both sides by 4. x = 268 cm / 4 x = 67 cm Therefore, the length of each side of the square is 67 cm. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 348 meters. Step 1: Define the perimeter of a square in terms of its side length. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the equation and solve for the side length. 348 meters = 4 × side length side length = 348 meters / 4 side length = 87 meters Therefore, the length of each side of the square is 87 meters. ### Answer: 87
Expected answer: 87
Correct? Yes
Problem: A square has a perimeter of 400m. What is the length of one of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 400 meters. Step 1: Set up the equation using the given information. 400 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 400 / 4 side length = 100 meters Therefore, the length of one side of the square is 100 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of the fourth side of the quadrilateral using the given information about the lengths of the other three sides and the perimeter. Given information: - Side lengths: 81m, 100m, and 19m. - Perimeter of the quadrilateral: 243m. Step 1: Find the sum of the known side lengths. Sum of the known side lengths = 81m + 100m + 19m = 200m Step 2: Find the length of the fourth side by subtracting the sum of the known side lengths from the perimeter. Length of the fourth side = Perimeter - Sum of the known side lengths Length of the fourth side = 243m - 200m = 43m Therefore, the length of the fourth side of the quadrilateral is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 186 cm. - One of the sides (let's call it the length) is 50 cm. Let's denote the other side (the width) as w. Substituting the given values into the perimeter formula, we get: 186 = 2 × (50 + w) 186 = 100 + 2w 2w = 186 - 100 2w = 86 w = 86/2 w = 43 Therefore, the other side (the width) of the rectangle is 43 cm long. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is given by: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 224 cm. - The length of one side is 78 cm. Let's denote the length of the adjacent side as x. Step 1: Substitute the given values into the perimeter formula. 224 = 2 × (78 + x) Step 2: Simplify the equation. 224 = 156 + 2x Step 3: Subtract 156 from both sides of the equation. 68 = 2x Step 4: Divide both sides by 2 to find the value of x. x = 68/2 x = 34 Therefore, the length of the adjacent side is 34 cm. ### Answer: 34
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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of the fourth side of the quadrilateral using the given information about the other three sides and the total perimeter. Given information: - Two sides measure 79 meters and 97 meters. - Another side measures 51 meters. - The total perimeter of the quadrilateral is 235 meters. Step 1: Find the sum of the lengths of the three known sides. Sum of the three known sides = 79 m + 97 m + 51 m = 227 m Step 2: Find the length of the fourth side by subtracting the sum of the three known sides from the total perimeter. Length of the fourth side = Total perimeter - Sum of the three known sides Length of the fourth side = 235 m - 227 m = 8 m Therefore, the length of the fourth side of the quadrilateral is 8 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 28 meters. Step 1: Set up the equation using the given information. 28 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 28 / 4 side length = 7 meters Therefore, the length of one side of the square with a perimeter of 28 meters is 7 meters. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 48cm. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 48 cm. Step 1: Set up the equation using the given information. 48 cm = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. Side length = 48 cm / 4 Side length = 12 cm Therefore, the length of each side of the square is 12 cm. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square plot of land is 184 meters. Step 1: Set up the equation using the given information. 184 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 184 / 4 side length = 46 meters Therefore, the length of one side of the square plot of land is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 56 meters. Step 1: Set up the equation using the given information. 56 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 56 / 4 side length = 14 meters 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of the fourth side of the quadrilateral using the given information about the perimeter and the lengths of the other three sides. Given information: - The perimeter of the quadrilateral is 157 meters. - One side is 97 meters long. - Another side is 5 meters long. - The third side is 30 meters long. Let's represent the length of the fourth side as x. According to the definition of perimeter, the sum of all four sides should be equal to the given perimeter. Perimeter = Sum of all four sides 157 m = 97 m + 5 m + 30 m + x Rearranging the terms, we get: x = 157 m - 97 m - 5 m - 30 m x = 157 m - 132 m x = 25 m Therefore, the length of the fourth side to complete the perimeter of the quadrilateral is 25 meters. ### 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?
Claude-3 Sonnet:
To find the length of the fourth side of a quadrilateral, we need to use the formula for the perimeter of a quadrilateral, which is the sum of all four sides. Given information: - The perimeter of the quadrilateral is 173 meters. - The lengths of the first, second, and third sides are 46 meters, 50 meters, and 35 meters, respectively. Let's denote the length of the fourth side as x. Perimeter of a quadrilateral = Sum of all four sides 173 = 46 + 50 + 35 + x Rearranging the terms, we get: 173 - 46 - 50 - 35 = x 173 - 131 = x x = 42 meters Therefore, the length of the fourth side of the quadrilateral is 42 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 72 cm. Step 1: Set up the equation using the given information. 72 cm = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 72 cm / 4 side length = 18 cm Therefore, the length of one side of the square is 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 352 meters. Step 1: Define the perimeter of a square. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Perimeter = 4 × side length Step 2: Set up an equation using the given information. 352 meters = 4 × side length Step 3: Solve for the side length. side length = 352 meters / 4 side length = 88 meters Therefore, the length of each side of the square is 88 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the width of the rectangle using the given information about its length and total perimeter. Given information: - Length of the rectangle = 23 meters - Total perimeter of the rectangle = 116 meters The formula for the perimeter of a rectangle is: Perimeter = 2 × (length + width) Substituting the given values, we get: 116 = 2 × (23 + width) 116 = 46 + 2 × width 70 = 2 × width 35 = width Therefore, the width of the rectangle is 35 meters. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The shape is a square. - The perimeter of the square is 124 meters. Step 1: Define the perimeter of a square. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Perimeter = 4 × side length Step 2: Set up an equation using the given information. Perimeter = 4 × side length 124 meters = 4 × side length Step 3: Solve for the side length. side length = 124 meters / 4 side length = 31 meters Therefore, the length of each side of the square is 31 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the property that the sum of the lengths of all sides of a quadrilateral is equal to its perimeter. Given information: - The total perimeter of the quadrilateral is 131 meters. - Three sides have lengths of 24 meters, 57 meters, and 17 meters. Let's represent the length of the fourth side as x. Step 1: Write an equation using the given information. 24 + 57 + 17 + x = 131 (Perimeter) Step 2: Simplify the equation. 98 + x = 131 Step 3: Solve for x by subtracting 98 from both sides. x = 131 - 98 x = 33 Therefore, the length of the fourth side of the quadrilateral is 33 meters. ### Answer: 33
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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 254 meters. - One of the sides (let's call it the length) is 89 meters. Let's denote the other side (the width) as x. Perimeter = 2 × (length + width) 254 = 2 × (89 + x) 254 = 178 + 2x 76 = 2x x = 38 Therefore, the length of the other side (the width) is 38 meters. ### Answer: 38
Expected answer: 38
Correct? Yes
Problem: A square has a perimeter of 208m. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 208 meters. Step 1: Write the formula for the perimeter of a square. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the formula and solve for the side length. 208 meters = 4 × side length side length = 208 meters / 4 side length = 52 meters Therefore, the length of each side of the square is 52 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 64 meters. Step 1: Set up the equation using the given information. 64 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 64 / 4 side length = 16 meters Therefore, the length of each side of the square is 16 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the given information about the perimeter and the lengths of three sides to find the length of the fourth side. Given information: - The total perimeter of the quadrilateral is 196 meters. - The lengths of three sides are 92 meters, 29 meters, and 62 meters. - The sum of the lengths of these three sides is 92 + 29 + 62 = 183 meters. Since the perimeter is the sum of all four side lengths, we can set up an equation: Perimeter = Sum of all side lengths 196 = 92 + 29 + 62 + x (where x is the length of the fourth side) Rearranging the equation, we get: x = 196 - (92 + 29 + 62) x = 196 - 183 x = 13 meters Therefore, the length of the fourth side of the quadrilateral is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 191 units. - One side is 35 units in length. - Another side is 76 units in length. - The third side is 5 units in length. Let's represent the length of the fourth side as x. Perimeter of the quadrilateral = Sum of the lengths of all four sides 191 = 35 + 76 + 5 + x Rearranging the terms, we get: 191 - 35 - 76 - 5 = x x = 75 units Therefore, the length of the fourth side of the quadrilateral 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 104 meters. The perimeter of a square is the total distance around the square, which is equal to four times the length of one side. Let's represent the length of one side as x. Perimeter of the square = 4 × x We know that the perimeter is 104 meters, so we can substitute this value into the equation: 104 = 4 × x x = 104 / 4 x = 26 Therefore, the length of each side of the square is 26 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 198 cm. - The length of the rectangle is 90 cm. Step 1: Substitute the known values into the perimeter formula. 198 = 2 × (90 + width) Step 2: Simplify the equation. 198 = 180 + 2 × width Step 3: Subtract 180 from both sides of the equation. 18 = 2 × width Step 4: Divide both sides of the equation by 2 to find the width. width = 18 / 2 width = 9 cm Therefore, the width of the rectangle is 9 cm. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle: P = 2(l + w), where P is the perimeter, l is the length, and w is the width. Given information: - The total perimeter of the rectangular garden is 128 feet. - One pair of opposite sides is 47 feet each. Let's denote the length of the remaining two opposite sides as x. Step 1: Set up the equation using the perimeter formula. 128 = 2(47 + x) Step 2: Simplify the equation. 128 = 94 + 2x Step 3: Subtract 94 from both sides. 34 = 2x Step 4: Divide both sides by 2 to find x. x = 17 Therefore, 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 356 meters. Step 1: Write the formula for the perimeter of a square. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the formula and solve for the side length. 356 meters = 4 × side length side length = 356 meters / 4 side length = 89 meters Therefore, the length of one side of the square is 89 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 236 units. - Two sides of the quadrilateral measure 89 units and 87 units, respectively. - The third side is 1 unit long. Let's denote the length of the fourth side as x. Using the perimeter formula, we can write: Perimeter = Sum of all four sides 236 = 89 + 87 + 1 + x Simplifying the equation: 236 = 177 + x x = 236 - 177 x = 59 Therefore, the length of the fourth side of the quadrilateral 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 340 meters. Step 1: Set up the equation using the given information. 340 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 340 / 4 side length = 85 meters Therefore, the length of each side of the square is 85 meters. ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: A square has a perimeter of 16m. What is the length of each side?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 16 meters. Step 1: Set up the equation using the given information. 16 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 16 / 4 side length = 4 meters Therefore, the length of each side of the square is 4 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of the fourth side of the quadrilateral using the given information about the lengths of the other three sides and the total perimeter. Given information: - The length of the first side is 1 meter. - The length of the second side is 54 meters. - The length of the third side is 9 meters. - The total perimeter of the quadrilateral is 81 meters. Step 1: Find the sum of the lengths of the three known sides. Sum of the lengths of the three known sides = 1 m + 54 m + 9 m = 64 m Step 2: Find the length of the fourth side by subtracting the sum of the lengths of the three known sides from the total perimeter. Length of the fourth side = Total perimeter - Sum of the lengths of the three known sides Length of the fourth side = 81 m - 64 m = 17 m Therefore, the length of the fourth side of the quadrilateral is 17 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square, given that the total perimeter is 316 meters. Given information: - The quadrilateral is a perfect square. - The total perimeter of the square is 316 meters. Step 1: Find the relationship between the perimeter and the side length of a square. Perimeter of a square = 4 × side length Step 2: Set up an equation using the given information. Perimeter of the square = 316 meters 4 × side length = 316 Step 3: Solve for the side length. 4 × side length = 316 side length = 316 / 4 side length = 79 meters Therefore, the length of each side of the square is 79 meters. ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 300m. How long is each side of the square?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 300 meters. Step 1: Set up the equation using the given information. 300 = 4 × side length Step 2: Solve for the side length by dividing both sides by 4. side length = 300 / 4 side length = 75 meters Therefore, each side of the square has a length of 75 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 198 meters. - Two sides have lengths of 19 meters and 57 meters, respectively. - Another side has a length of 22 meters. Let's represent the unknown side length as x. Perimeter = Sum of all side lengths 198 = 19 + 57 + 22 + x 198 = 98 + x x = 198 - 98 x = 100 meters Therefore, the length of the remaining side of the quadrilateral is 100 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the length of one side of the square given its perimeter. Given information: - The perimeter of the square is 172 meters. Step 1: Write the formula for the perimeter of a square. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the formula and solve for the side length. 172 meters = 4 × side length side length = 172 meters / 4 side length = 43 meters Therefore, the length of each side of the square is 43 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the relationship between the perimeter of a square and the length of its sides. Given information: - The shape is a square. - The perimeter of the square is 304 cm. Step 1: Find the formula for the perimeter of a square. Perimeter of a square = 4 × side length Step 2: Substitute the given perimeter value into the formula and solve for the side length. 304 cm = 4 × side length Side length = 304 cm / 4 Side length = 76 cm Therefore, the length of one side of the square is 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The total perimeter of the rectangle is 158 meters. - The length of each shorter side (width) is 51 meters. Let's denote the length of each longer side as x. Step 1: Substitute the given values into the perimeter formula. 158 = 2 × (x + 51) Step 2: Simplify the equation. 158 = 2x + 102 Step 3: Subtract 102 from both sides of the equation. 158 - 102 = 2x + 102 - 102 56 = 2x Step 4: Divide both sides of the equation by 2 to find the value of x. 56/2 = 2x/2 28 = x Therefore, the length of each longer side of the rectangle 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 72 meters. Step 1: Set up the equation using the given information. 72 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 72 / 4 side length = 18 meters Therefore, the length of one side of the square is 18 meters. ### 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?
Claude-3 Sonnet:
To solve this problem, we need to find the lengths of the other two sides of the rectangular playground using the given information. Given information: - Two opposite sides of the fence are 19 meters each. - The total length of the fence is 166 meters. Let's denote the lengths of the other two sides as x and y. Step 1: Express the total length of the fence in terms of x and y. Total length of the fence = Sum of all four sides 166 meters = 19 meters + 19 meters + x + y 166 meters = 38 meters + x + y Step 2: Rearrange the equation to isolate x and y. x + y = 166 meters - 38 meters x + y = 128 meters Step 3: Since the playground is rectangular, the opposite sides have equal lengths. Therefore, x = y. x = y Step 4: Substitute x = y into the equation from Step 2. x + x = 128 meters 2x = 128 meters x = 128 meters / 2 x = 64 meters Therefore, the length of each of the other two sides is 64 meters. ### Answer: 64
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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 246 meters. - Two sides have lengths of 40 meters and 32 meters. - One side has a length of 95 meters. Let's represent the unknown length of the fourth side as x. Perimeter = Sum of all four sides 246 = 40 + 32 + 95 + x 246 = 167 + x x = 246 - 167 x = 79 meters Therefore, the length of the fourth side of the quadrilateral is 79 meters. ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 32m. What is the length of one of its sides?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a square, which is: Perimeter = 4 × side length Given information: - The perimeter of the square is 32 meters. Step 1: Set up the equation using the given information. 32 = 4 × side length Step 2: Divide both sides of the equation by 4 to find the side length. side length = 32 / 4 side length = 8 meters Therefore, the length of one side of the square is 8 meters. ### 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?
Claude-3 Sonnet:
To find the length of one side of a square, given its perimeter, we can use the following steps: 1. The perimeter of a square is the total distance around the square, which is the sum of the lengths of all four sides. 2. Since all sides of a square are equal, we can represent the length of one side as x. 3. The perimeter formula for a square is: Perimeter = 4 × x (since there are four sides of equal length). 4. Given information: The perimeter of the square is 12 meters. 5. Substituting the given value in the formula: 12 = 4 × x 6. Dividing both sides by 4: x = 12 / 4 7. Simplifying: x = 3 Therefore, the length of one side of the square with a perimeter of 12 meters 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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given information: - The perimeter of the quadrilateral is 160 meters. - The lengths of three sides are 29 meters, 16 meters, and 41 meters. Let's represent the unknown length of the fourth side as x. Perimeter = Sum of all four sides 160 m = 29 m + 16 m + 41 m + x Rearranging the terms, we get: x = 160 m - (29 m + 16 m + 41 m) x = 160 m - 86 m x = 74 m Therefore, the length of the fourth side of the quadrilateral is 74 meters. ### Answer: 74
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?
Claude-3 Sonnet:
To solve this problem, we need to use the formula for the perimeter of a rectangle, which is: Perimeter = 2 × (length + width) Given information: - The perimeter of the rectangle is 98 meters. - One of the sides (let's call it the width) is 5 meters. Let's denote the length of the other side as x. Perimeter = 2 × (length + width) 98 = 2 × (x + 5) 98 = 2x + 10 88 = 2x x = 44 Therefore, the length of the other side is 44 meters. ### Answer: 44
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?
Claude-3 Sonnet:
To solve this problem, we need to find the lengths of the other two sides of the rectangle using the given information about the perimeter and the lengths of two sides. Given information: - Two sides of the rectangle measure 45 meters each. - The total perimeter of the rectangle is 210 meters. Step 1: Find the sum of the lengths of the two known sides. Sum of the lengths of the two known sides = 45 meters + 45 meters = 90 meters Step 2: Find the sum of the lengths of the remaining two sides by subtracting the sum of the known sides from the total perimeter. Sum of the lengths of the remaining two sides = Total perimeter - Sum of the lengths of the known sides Sum of the lengths of the remaining two sides = 210 meters - 90 meters = 120 meters Step 3: Since the rectangle has two equal pairs of opposite sides, the lengths of the remaining two sides are equal. Length of each of the remaining two sides = Sum of the lengths of the remaining two sides / 2 Length of each of the remaining two sides = 120 meters / 2 = 60 meters Therefore, the length of each of the other two sides of the rectangle is 60 meters. ### Answer: 60
Expected answer: 60
Correct? Yes