GPT-4o 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?
GPT-4o:
To find the width of the pool, we start by using the formula for the perimeter of a rectangle:
\[ P = 2L + 2W \]
where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width. We are given:
\[ P = 324 \, \text{meters} \]
\[ L = 83 \, \text{meters} \]
Substituting these values into the perimeter formula, we get:
\[ 324 = 2(83) + 2W \]
First, calculate \( 2 \times 83 \):
\[ 2 \times 83 = 166 \]
So the equation becomes:
\[ 324 = 166 + 2W \]
Next, isolate \( 2W \) by subtracting 166 from both sides:
\[ 324 - 166 = 2W \]
\[ 158 = 2W \]
Finally, solve for \( W \) by dividing both sides by 2:
\[ W = \frac{158}{2} \]
\[ W = 79 \]
### Answer: 79 meters
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 40m. What is the length of each side?
GPT-4o:
To find the length of each side of a square, we need to use the formula for the perimeter of a square. The formula is:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 40 meters, we can set up the equation:
\[ 4 \times \text{side length} = 40 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{40}{4} \]
\[ \text{side length} = 10 \]
### Answer: 10 meters
Expected answer: 10
Correct? Yes
Problem: A square has a perimeter of 344m. What is the length of each side of the square?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 344 meters, we can set up the equation:
\[ 4s = 344 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{344}{4} \]
\[ s = 86 \]
So, the length of each side of the square is 86 meters.
### Answer: 86 meters
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 348m. What would be the length of each side of the square?
GPT-4o:
To find the length of each side of the square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 348 meters, we can set up the equation:
\[ 4s = 348 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{348}{4} \]
Now, we perform the division:
\[ s = 87 \]
So, the length of each side of the square is 87 meters.
### Answer: 87 meters
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?
GPT-4o:
To determine the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle. The perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{width}) \]
We are given:
- The perimeter \( P = 194 \) cm
- The length of one side \( \text{length} = 49 \) cm
Let's denote the width of the rectangle as \( w \). Plugging the known values into the perimeter formula, we get:
\[ 194 = 2 \times (49 + w) \]
First, we simplify the equation by dividing both sides by 2:
\[ 97 = 49 + w \]
Next, we solve for \( w \) by subtracting 49 from both sides:
\[ w = 97 - 49 \]
\[ w = 48 \]
Thus, 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?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side.
Given that the perimeter \( P \) is 192 meters, we can set up the equation:
\[ 4s = 192 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{192}{4} \]
\[ s = 48 \]
### Answer: 48 meters
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square, which is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 68 cm, we can set up the equation:
\[ 4 \times \text{side length} = 68 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{68}{4} \]
\[ \text{side length} = 17 \]
### 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?
GPT-4o:
To find the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle: \[ P = 2 \times (L + W) \] where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width. We are given that the perimeter \( P \) is 52 meters and one of the sides (let's assume it's the width \( W \)) is 4 meters. First, we substitute the known values into the perimeter formula: \[ 52 = 2 \times (L + 4) \] Next, we solve for \( L \): 1. Divide both sides by 2 to isolate the term with \( L \): \[ 26 = L + 4 \] 2. Subtract 4 from both sides to solve for \( L \): \[ L = 26 - 4 \] \[ L = 22 \] So, the length of the other side is 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides:
\[ 93 \, \text{m} + 98 \, \text{m} + 36 \, \text{m} = 227 \, \text{m} \]
Next, we subtract this sum from the total perimeter of the quadrilateral:
\[ 229 \, \text{m} - 227 \, \text{m} = 2 \, \text{m} \]
Thus, the length of the fourth side is:
### 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?
GPT-4o:
To find the length of each side of the square, we need to use the formula for the perimeter of a square, which is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 16 meters, we can set up the equation:
\[ 16 = 4 \times \text{side length} \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{16}{4} \]
\[ \text{side length} = 4 \]
### Answer: 4 meters
Expected answer: 4
Correct? Yes
Problem: A square has a perimeter of 272m. What is the length of each side of the square?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 272 meters, we can set up the equation:
\[ 4s = 272 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{272}{4} \]
\[ s = 68 \]
### Answer: 68 meters
Expected answer: 68
Correct? Yes
Problem: A square has a perimeter of 244m. What is the length of each side of the square?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 244 meters, we can set up the equation:
\[ 4s = 244 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{244}{4} \]
\[ s = 61 \]
So, the length of each side of the square is 61 meters.
### Answer: 61 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to subtract the sum of the lengths of the three known sides from the total perimeter.
First, we add the lengths of the three known sides:
\[ 70 \, \text{m} + 29 \, \text{m} + 61 \, \text{m} = 160 \, \text{m} \]
Next, we subtract this sum from the total perimeter:
\[ 227 \, \text{m} - 160 \, \text{m} = 67 \, \text{m} \]
Therefore, the length of the fourth side is:
### 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?
GPT-4o:
To find the length of the side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 280 meters, we can set up the equation:
\[ 4s = 280 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{280}{4} \]
\[ s = 70 \]
So, the length of the side of the square is 70 meters.
### Answer: 70 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides:
\[ 37 \, \text{cm} + 98 \, \text{cm} + 41 \, \text{cm} \]
First, add 37 cm and 98 cm:
\[ 37 + 98 = 135 \, \text{cm} \]
Next, add the result to 41 cm:
\[ 135 + 41 = 176 \, \text{cm} \]
The total length of the three known sides is 176 cm. The perimeter of the quadrilateral is given as 219 cm. To find the length of the fourth side, we subtract the total length of the three known sides from the perimeter:
\[ 219 \, \text{cm} - 176 \, \text{cm} = 43 \, \text{cm} \]
### Answer: 43 cm
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side.
Given that the perimeter \( P \) is 44 meters, we can set up the equation:
\[ 4s = 44 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{44}{4} \]
\[ s = 11 \]
### Answer: 11 meters
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?
GPT-4o:
To find the length of the shorter side of the rectangular garden, we start by using the formula for the perimeter of a rectangle: \[ P = 2 \times (L + W) \] where \( P \) is the perimeter, \( L \) is the length of the longer side, and \( W \) is the width (shorter side). Given: - Perimeter \( P = 282 \) meters - Length \( L = 71 \) meters We can substitute these values into the perimeter formula: \[ 282 = 2 \times (71 + W) \] First, divide both sides of the equation by 2 to isolate the sum of the length and width: \[ 141 = 71 + W \] Next, solve for \( W \) by subtracting 71 from both sides: \[ W = 141 - 71 \] \[ W = 70 \] Thus, the length of the shorter side is 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?
GPT-4o:
To find the length of the other side of the rectangular garden, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter is 128 meters and the shorter side (width) is 57 meters, we can set up the equation as follows:
\[ 128 = 2 \times (\text{length} + 57) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and the width:
\[ 64 = \text{length} + 57 \]
Next, we subtract 57 from both sides to solve for the length:
\[ \text{length} = 64 - 57 \]
\[ \text{length} = 7 \]
Thus, the length of the other side of the garden 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 392 meters, we can set up the equation:
\[ 4s = 392 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{392}{4} \]
\[ s = 98 \]
So, the length of each side of the square is 98 meters.
### Answer: 98 meters
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?
GPT-4o:
To find the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter is 204 meters and one side (length) is 16 meters, we can set up the equation as follows:
\[ 204 = 2 \times (16 + \text{width}) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 102 = 16 + \text{width} \]
Next, we subtract 16 from both sides to solve for the width:
\[ \text{width} = 102 - 16 \]
\[ \text{width} = 86 \]
Thus, the length of the other side is 86 meters.
### Answer: 86 meters
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 336cm. What is the length of one of its sides?
GPT-4o:
To find the length of one side of a square given its perimeter, we use the formula for the perimeter of a square:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 336 cm, we can set up the equation:
\[ 4 \times \text{side length} = 336 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{336}{4} \]
\[ \text{side length} = 84 \]
### Answer: 84 cm
Expected answer: 84
Correct? Yes
Problem: A square has a perimeter of 144 meters. What is the length of one side of the square?
GPT-4o:
To find the length of one side of the square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 144 meters, we can set up the equation:
\[ 4s = 144 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{144}{4} \]
\[ s = 36 \]
### 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by using the given information about the perimeter and the lengths of the other three sides.
The perimeter of the quadrilateral is the sum of the lengths of all four sides. We can set up the equation as follows:
\[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \]
Given:
- Perimeter = 236 cm
- Side 1 = 69 cm
- Side 2 = 50 cm
- Side 3 = 39 cm
Let \( \text{Side 4} \) be \( x \). Then we have:
\[ 236 = 69 + 50 + 39 + x \]
First, we add the known side lengths:
\[ 69 + 50 + 39 = 158 \]
Now, substitute this sum back into the equation:
\[ 236 = 158 + x \]
To find \( x \), we subtract 158 from both sides of the equation:
\[ x = 236 - 158 \]
\[ x = 78 \]
Therefore, the length of the fourth side is 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?
GPT-4o:
To find the length of the unknown side of the quadrilateral, we start by using the given information about the perimeter and the lengths of the known sides.
The perimeter of the quadrilateral is the sum of all its sides:
\[ \text{Perimeter} = 193 \text{ cm} \]
The known side lengths are:
\[ 37 \text{ cm}, 14 \text{ cm}, \text{ and } 73 \text{ cm} \]
Let the unknown side length be \( x \). The sum of all the sides is:
\[ 37 \text{ cm} + 14 \text{ cm} + 73 \text{ cm} + x = 193 \text{ cm} \]
We can set up the equation:
\[ 37 + 14 + 73 + x = 193 \]
First, add the known side lengths:
\[ 37 + 14 = 51 \]
\[ 51 + 73 = 124 \]
So the equation becomes:
\[ 124 + x = 193 \]
To find \( x \), subtract 124 from both sides:
\[ x = 193 - 124 \]
\[ x = 69 \]
### Answer: 69 cm
Expected answer: 69
Correct? Yes
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 160 meters, we can set up the equation:
\[ 4s = 160 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{160}{4} \]
\[ s = 40 \]
### Answer: 40 meters
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?
GPT-4o:
To find the width of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \]
Given that the perimeter is 228 meters and the length is 90 meters, we can substitute these values into the formula:
\[ 228 = 2 \times (90 + \text{Width}) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 114 = 90 + \text{Width} \]
Next, we solve for the width by subtracting 90 from both sides:
\[ \text{Width} = 114 - 90 \]
\[ \text{Width} = 24 \]
### 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?
GPT-4o:
To find the length of one side of the square field, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 136 meters, we can set up the equation:
\[ 4s = 136 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{136}{4} \]
\[ s = 34 \]
So, the length of one side of the square field is 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?
GPT-4o:
To determine the length of the opposite side of the rectangle, we start by using the formula for the perimeter of a rectangle. The perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter \( P \) is 236 meters and one side (let's call it the length \( L \)) is 43 meters, we can set up the equation as follows:
\[ 236 = 2 \times (43 + \text{width}) \]
First, we simplify inside the parentheses:
\[ 236 = 2 \times (43 + W) \]
Next, we divide both sides of the equation by 2 to isolate the term inside the parentheses:
\[ 118 = 43 + W \]
Now, we solve for \( W \) (the width):
\[ W = 118 - 43 \]
\[ W = 75 \]
So, the length of the opposite side (the width) is 75 meters.
### Answer: 75 meters
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?
GPT-4o:
To find the length of the missing side of the quadrilateral, we first need to sum the lengths of the known sides and then subtract this sum from the total perimeter.
Given:
- Total perimeter of the quadrilateral = 206 meters
- Length of two sides together = 58 meters
- Length of the third side = 54 meters
- Length of the fourth side = 1 meter
First, we add the lengths of the known sides:
\[ 58 + 54 + 1 = 113 \text{ meters} \]
Next, we subtract this sum from the total perimeter to find the length of the missing side:
\[ 206 - 113 = 93 \text{ meters} \]
### Answer: 93 meters
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?
GPT-4o:
To find the length of each side of the square field, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 284 meters, we can set up the equation:
\[ 4s = 284 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{284}{4} \]
\[ s = 71 \]
So, the length of each side of the square field is 71 meters.
### 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?
GPT-4o:
To find the width of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ P = 2L + 2W \]
where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width. We are given:
\[ P = 150 \text{ feet} \]
\[ L = 69 \text{ feet} \]
Substituting these values into the perimeter formula, we get:
\[ 150 = 2(69) + 2W \]
First, calculate \( 2 \times 69 \):
\[ 2 \times 69 = 138 \]
So the equation becomes:
\[ 150 = 138 + 2W \]
Next, isolate \( 2W \) by subtracting 138 from both sides:
\[ 150 - 138 = 2W \]
\[ 12 = 2W \]
Now, solve for \( W \) by dividing both sides by 2:
\[ W = \frac{12}{2} \]
\[ W = 6 \]
### 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?
GPT-4o:
To find the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ P = 2 \times (L + W) \]
where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width.
Given:
\[ P = 166 \, \text{m} \]
\[ L = 35 \, \text{m} \]
We need to find \( W \). Plugging the given values into the perimeter formula, we get:
\[ 166 = 2 \times (35 + W) \]
First, divide both sides by 2 to isolate the sum of the length and width:
\[ \frac{166}{2} = 35 + W \]
\[ 83 = 35 + W \]
Next, subtract 35 from both sides to solve for \( W \):
\[ 83 - 35 = W \]
\[ 48 = W \]
So, the other side of the rectangle is 48 meters long.
### Answer: 48 meters
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 124 meters, we can set up the equation:
\[ 4s = 124 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{124}{4} \]
\[ s = 31 \]
So, the length of each side of the square is 31 meters.
### Answer: 31 meters
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?
GPT-4o:
To find the length of the opposite side of the rectangular field, we need to use the formula for the perimeter of a rectangle. The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{width}) \]
Given:
- The perimeter \( P \) is 336 feet.
- The length of one side is 79 feet.
Let's denote the length by \( L \) and the width by \( W \). We know that:
\[ L = 79 \text{ feet} \]
Substituting the known values into the perimeter formula:
\[ 336 = 2 \times (79 + W) \]
First, divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 168 = 79 + W \]
Next, solve for \( W \) by subtracting 79 from both sides:
\[ W = 168 - 79 \]
\[ W = 89 \]
Therefore, the length of the opposite side (which is the width in this context) is 89 feet.
### Answer: 89 feet
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?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 132 meters, we can set up the equation:
\[ 4s = 132 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{132}{4} \]
\[ s = 33 \]
So, the length of one side of the square 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?
GPT-4o:
To find the width of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ P = 2L + 2W \]
where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width. We are given:
\[ P = 138 \text{ feet} \]
\[ L = 46 \text{ feet} \]
Substituting these values into the perimeter formula, we get:
\[ 138 = 2(46) + 2W \]
First, calculate \( 2 \times 46 \):
\[ 2 \times 46 = 92 \]
So the equation becomes:
\[ 138 = 92 + 2W \]
Next, subtract 92 from both sides to isolate \( 2W \):
\[ 138 - 92 = 2W \]
\[ 46 = 2W \]
Finally, divide both sides by 2 to solve for \( W \):
\[ W = \frac{46}{2} \]
\[ W = 23 \]
### 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?
GPT-4o:
To find the width of the rectangular field, we start by using the formula for the perimeter of a rectangle. The formula is:
\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \]
Given that the perimeter is 200 meters and the length is 49 meters, we can substitute these values into the formula:
\[ 200 = 2 \times (49 + \text{Width}) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and the width:
\[ 100 = 49 + \text{Width} \]
Next, we subtract 49 from both sides to solve for the width:
\[ \text{Width} = 100 - 49 \]
\[ \text{Width} = 51 \]
### Answer: 51 meters
Expected answer: 51
Correct? Yes
Problem: A square has a perimeter of 200m. What is the length of each side?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 200 meters, we can set up the equation:
\[ 4s = 200 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{200}{4} \]
\[ s = 50 \]
So, the length of each side of the square is 50 meters.
### Answer: 50 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to subtract the sum of the known three sides from the total perimeter.
First, let's add the lengths of the three known sides:
\[ 9 \, \text{m} + 30 \, \text{m} + 71 \, \text{m} = 110 \, \text{m} \]
Next, we subtract this sum from the total perimeter:
\[ 199 \, \text{m} - 110 \, \text{m} = 89 \, \text{m} \]
Therefore, the length of the fourth side is:
### 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides:
\[ 35 \, \text{m} + 62 \, \text{m} + 70 \, \text{m} = 167 \, \text{m} \]
Next, we subtract this sum from the total perimeter of the quadrilateral to find the length of the fourth side:
\[ 207 \, \text{m} - 167 \, \text{m} = 40 \, \text{m} \]
### 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?
GPT-4o:
To find the length of the longer sides of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter is 384 cm and one of the shorter sides (width) is 99 cm, we can set up the equation as follows:
\[ 384 = 2 \times (\text{length} + 99) \]
First, divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 192 = \text{length} + 99 \]
Next, subtract 99 from both sides to solve for the length:
\[ \text{length} = 192 - 99 \]
\[ \text{length} = 93 \]
Therefore, the length of the longer sides of the rectangle is 93 cm.
### Answer: 93 cm
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the first three sides and then subtracting this sum from the total perimeter.
First, we add the lengths of the first three sides:
\[ 78 \, \text{m} + 15 \, \text{m} + 63 \, \text{m} = 156 \, \text{m} \]
Next, we subtract this sum from the total perimeter to find the length of the fourth side:
\[ 255 \, \text{m} - 156 \, \text{m} = 99 \, \text{m} \]
### 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?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 128 meters, we can set up the equation:
\[ 4s = 128 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{128}{4} \]
\[ s = 32 \]
### Answer: 32 meters
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?
GPT-4o:
To find the length of the other pair of opposite sides of the rectangle, we start by using the formula for the perimeter of a rectangle. The perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{width}) \]
We know the perimeter is 96 feet, and one pair of opposite sides (the length) is 33 feet each. Let's denote the unknown width by \( w \).
Substituting the known values into the perimeter formula, we get:
\[ 96 = 2 \times (33 + w) \]
First, we divide both sides of the equation by 2:
\[ 48 = 33 + w \]
Next, we solve for \( w \) by subtracting 33 from both sides:
\[ w = 48 - 33 \]
\[ w = 15 \]
Thus, the length of the other pair of opposite sides (the width) is 15 feet.
### Answer: 15 feet
Expected answer: 15
Correct? Yes
Problem: The perimeter of a square field is 112 meters. What is the length of each side?
GPT-4o:
To find the length of each side of the square field, we need to use the formula for the perimeter of a square. The formula for the perimeter \( P \) of a square with side length \( s \) is:
\[ P = 4s \]
Given that the perimeter is 112 meters, we can set up the equation:
\[ 4s = 112 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{112}{4} \]
\[ s = 28 \]
So, the length of each side of the square field is 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?
GPT-4o:
To find the length of one side of a square when given the perimeter, we use the formula for the perimeter of a square:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 32 cm, we can set up the equation:
\[ 32 = 4 \times \text{side length} \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{32}{4} \]
\[ \text{side length} = 8 \]
### 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 364 meters, we can set up the equation:
\[ 4s = 364 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{364}{4} \]
Now, we perform the division:
\[ s = 91 \]
So, the length of each side of the square is 91 meters.
### Answer: 91 meters
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?
GPT-4o:
To find the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \]
Given that the total perimeter is 144 feet and the length of one side (Length) is 38 feet, we can set up the equation:
\[ 144 = 2 \times (38 + \text{Width}) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 72 = 38 + \text{Width} \]
Next, we solve for the width by subtracting 38 from both sides:
\[ \text{Width} = 72 - 38 \]
\[ \text{Width} = 34 \]
Thus, the length of the other side of the rectangle is 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?
GPT-4o:
To find the length of the remaining side, we first need to sum the known side lengths and then subtract this sum from the total perimeter. The known side lengths are: - Two sides that add up to 54 meters. - One side that is 22 meters. - One side that is 37 meters. First, we add these known side lengths together: \[ 54 + 22 + 37 \] Calculating the sum: \[ 54 + 22 = 76 \] \[ 76 + 37 = 113 \] Now, we subtract this sum from the total perimeter to find the length of the remaining side: \[ 205 - 113 = 92 \] ### Answer: 92 meters
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?
GPT-4o:
To find the width of the rectangular field, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \]
Given:
- Perimeter = 174 meters
- Length = 65 meters
We can substitute these values into the formula:
\[ 174 = 2 \times (65 + \text{Width}) \]
First, divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ \frac{174}{2} = 65 + \text{Width} \]
\[ 87 = 65 + \text{Width} \]
Next, subtract 65 from both sides to solve for the width:
\[ 87 - 65 = \text{Width} \]
\[ 22 = \text{Width} \]
### Answer: 22 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides:
\[ 25 \, \text{cm} + 17 \, \text{cm} + 89 \, \text{cm} = 131 \, \text{cm} \]
Next, we subtract this sum from the total perimeter of the quadrilateral to find the length of the fourth side:
\[ 176 \, \text{cm} - 131 \, \text{cm} = 45 \, \text{cm} \]
### Answer: 45 cm
Expected answer: 45
Correct? Yes
Problem: A square has a perimeter of 372 meters. What is the length of each side?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 372 meters, we can set up the equation:
\[ 4 \times \text{side length} = 372 \]
Next, we solve for the side length by dividing both sides of the equation by 4:
\[ \text{side length} = \frac{372}{4} \]
Performing the division:
\[ \text{side length} = 93 \]
So, 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?
GPT-4o:
To find the length of one side of a square field, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 240 meters, we can set up the equation:
\[ 4s = 240 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{240}{4} \]
\[ s = 60 \]
So, the length of one side of the square field is 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?
GPT-4o:
To determine the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle: \[ P = 2 \times (L + W) \] where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width. Given that the perimeter \( P \) is 242 meters and one of the sides (let's assume it's the length \( L \)) is 97 meters, we can set up the equation as follows: \[ 242 = 2 \times (97 + W) \] First, we divide both sides of the equation by 2 to isolate the sum of the length and width: \[ 121 = 97 + W \] Next, we solve for \( W \) by subtracting 97 from both sides: \[ W = 121 - 97 \] \[ W = 24 \] Thus, the length of the other side 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?
GPT-4o:
To determine the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 316 meters, we can set up the equation:
\[ 4s = 316 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{316}{4} \]
Now, we perform the division:
\[ s = 79 \]
Thus, 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 268 cm, we can set up the equation:
\[ 4s = 268 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{268}{4} \]
\[ s = 67 \]
So, the length of each side of the square is 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 348 meters, we can set up the equation:
\[ 4s = 348 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{348}{4} \]
Now, we perform the division:
\[ s = 87 \]
So, the length of each side of the square is 87 meters.
### Answer: 87 meters
Expected answer: 87
Correct? Yes
Problem: A square has a perimeter of 400m. What is the length of one of its sides?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side.
Given that the perimeter \( P \) is 400 meters, we can set up the equation:
\[ 4s = 400 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{400}{4} \]
\[ s = 100 \]
### Answer: 100 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to use the formula for the perimeter of a quadrilateral, which is the sum of the lengths of all four sides. Given: - Lengths of three sides: 81m, 100m, and 19m - Perimeter of the quadrilateral: 243m Let the length of the fourth side be \( x \). The perimeter is the sum of all four sides: \[ 81 + 100 + 19 + x = 243 \] First, add the known side lengths: \[ 81 + 100 = 181 \] \[ 181 + 19 = 200 \] Now, set up the equation: \[ 200 + x = 243 \] To find \( x \), subtract 200 from both sides: \[ x = 243 - 200 \] \[ x = 43 \] ### 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?
GPT-4o:
To find the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter is 186 cm and one side (let's call it the length) is 50 cm, we can set up the equation as follows:
\[ 186 = 2 \times (50 + \text{width}) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and the width:
\[ 93 = 50 + \text{width} \]
Next, we subtract 50 from both sides to solve for the width:
\[ \text{width} = 93 - 50 \]
\[ \text{width} = 43 \]
Thus, the other side of the rectangle is 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?
GPT-4o:
To find the length of the adjacent side of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \]
Given that the perimeter is 224 cm and the length is 78 cm, we can substitute these values into the formula:
\[ 224 = 2 \times (78 + \text{Width}) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 112 = 78 + \text{Width} \]
Next, we solve for the width by subtracting 78 from both sides:
\[ \text{Width} = 112 - 78 \]
\[ \text{Width} = 34 \]
Thus, 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to use the information given about the perimeter and the lengths of the other three sides. The perimeter of the quadrilateral is the sum of the lengths of all four sides. We are given: - Side 1 = 79 meters - Side 2 = 97 meters - Side 3 = 51 meters - Perimeter = 235 meters Let the length of the fourth side be \( x \) meters. The equation for the perimeter is: \[ 79 + 97 + 51 + x = 235 \] First, we add the lengths of the three known sides: \[ 79 + 97 + 51 = 227 \] Next, we solve for \( x \) by subtracting the sum of the known sides from the total perimeter: \[ x = 235 - 227 \] \[ x = 8 \] ### Answer: 8 meters
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?
GPT-4o:
To find the length of one side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 28 meters, we can set up the equation:
\[ 4s = 28 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{28}{4} \]
\[ s = 7 \]
### Answer: 7 meters
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 48cm. What is the length of each side?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square, which is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 48 cm, we can set up the equation:
\[ 4 \times \text{side length} = 48 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{48}{4} \]
\[ \text{side length} = 12 \]
### Answer: 12 cm
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?
GPT-4o:
To find the length of one side of a square plot of land, we start with the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 184 meters, we can set up the equation:
\[ 4s = 184 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{184}{4} \]
\[ s = 46 \]
So, the length of one side of the square plot of land is 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter is 56 meters, we can set up the equation:
\[ 4s = 56 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{56}{4} \]
\[ s = 14 \]
So, the length of each side of the square is 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to subtract the lengths of the known three sides from the total perimeter.
Given:
- Perimeter of the quadrilateral = 157 meters
- Length of the first side = 97 meters
- Length of the second side = 5 meters
- Length of the third side = 30 meters
First, we sum the lengths of the three known sides:
\[ 97 + 5 + 30 = 132 \text{ meters} \]
Next, we subtract this sum from the total perimeter to find the length of the fourth side:
\[ 157 - 132 = 25 \text{ meters} \]
### Answer: 25 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to subtract the sum of the lengths of the first three sides from the total perimeter.
First, we add the lengths of the first three sides:
\[ 46 \, \text{m} + 50 \, \text{m} + 35 \, \text{m} = 131 \, \text{m} \]
Next, we subtract this sum from the total perimeter:
\[ 173 \, \text{m} - 131 \, \text{m} = 42 \, \text{m} \]
Therefore, the length of the fourth side is:
### 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?
GPT-4o:
To find the length of one side of the square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 72 cm, we can set up the equation:
\[ 4s = 72 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{72}{4} \]
\[ s = 18 \]
### 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 352 meters, we can set up the equation:
\[ 4s = 352 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{352}{4} \]
\[ s = 88 \]
So, the length of each side of the square is 88 meters.
### Answer: 88 meters
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?
GPT-4o:
To find the width of the rectangle, we start by using the formula for the perimeter of a rectangle: \[ P = 2 \times (L + W) \] where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width. We are given: - \( P = 116 \) meters - \( L = 23 \) meters Substituting the given values into the perimeter formula: \[ 116 = 2 \times (23 + W) \] First, divide both sides of the equation by 2 to isolate the sum of the length and width: \[ 58 = 23 + W \] Next, subtract 23 from both sides to solve for \( W \): \[ W = 58 - 23 \] \[ W = 35 \] ### Answer: 35 meters
Expected answer: 35
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 124 meters, we can set up the equation:
\[ 4s = 124 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{124}{4} \]
\[ s = 31 \]
So, the length of each side of the square is 31 meters.
### Answer: 31 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides:
\[ 24 \, \text{m} + 57 \, \text{m} + 17 \, \text{m} = 98 \, \text{m} \]
Next, we subtract this sum from the total perimeter of the quadrilateral:
\[ 131 \, \text{m} - 98 \, \text{m} = 33 \, \text{m} \]
Thus, the length of the fourth side is:
### 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?
GPT-4o:
To find the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter is 254 meters and one of the sides (length) is 89 meters, we can set up the equation as follows:
\[ 254 = 2 \times (89 + \text{width}) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 127 = 89 + \text{width} \]
Next, we solve for the width by subtracting 89 from both sides:
\[ \text{width} = 127 - 89 \]
\[ \text{width} = 38 \]
Thus, the length of the other side is 38 meters.
### Answer: 38 meters
Expected answer: 38
Correct? Yes
Problem: A square has a perimeter of 208m. What is the length of each side?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 208 meters, we can set up the equation:
\[ 4s = 208 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{208}{4} \]
\[ s = 52 \]
So, the length of each side of the square is 52 meters.
### Answer: 52 meters
Expected answer: 52
Correct? Yes
Problem: A square has a perimeter of 64m. What is the length of each side of the square?
GPT-4o:
To find the length of each side of a square given its perimeter, we use the formula for the perimeter of a square:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 64 meters, we can set up the equation:
\[ 4 \times \text{side length} = 64 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{64}{4} \]
\[ \text{side length} = 16 \]
### Answer: 16 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by noting the total perimeter and the lengths of the three known sides.
The total perimeter of the quadrilateral is 196 meters.
The lengths of the three known sides are:
- First side: 92 meters
- Second side: 29 meters
- Third side: 62 meters
First, we sum the lengths of the three known sides:
\[ 92 + 29 + 62 = 183 \text{ meters} \]
Since the total perimeter is the sum of all four sides, we can find the length of the fourth side by subtracting the sum of the three known sides from the total perimeter:
\[ 196 - 183 = 13 \text{ meters} \]
Thus, the length of the fourth side is:
### 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to subtract the sum of the known three sides from the total perimeter. First, let's add the lengths of the three known sides: \[ 35 + 76 + 5 = 116 \] Next, we subtract this sum from the total perimeter: \[ 191 - 116 = 75 \] Thus, the length of the fourth side is: ### Answer: 75 units.
Expected answer: 75
Correct? Yes
Problem: A square has a perimeter of 104m. What is the length of each side?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square, which is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 104 meters, we can set up the equation:
\[ 4 \times \text{side length} = 104 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{104}{4} \]
\[ \text{side length} = 26 \]
### Answer: 26 meters
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?
GPT-4o:
To find the width of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ P = 2L + 2W \]
where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width.
Given:
\[ P = 198 \, \text{cm} \]
\[ L = 90 \, \text{cm} \]
Substitute the given values into the perimeter formula:
\[ 198 = 2(90) + 2W \]
First, calculate \( 2 \times 90 \):
\[ 2 \times 90 = 180 \]
Now, substitute this back into the equation:
\[ 198 = 180 + 2W \]
Next, isolate \( 2W \) by subtracting 180 from both sides:
\[ 198 - 180 = 2W \]
\[ 18 = 2W \]
Finally, solve for \( W \) by dividing both sides by 2:
\[ W = \frac{18}{2} \]
\[ W = 9 \, \text{cm} \]
### 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?
GPT-4o:
To find the length of the remaining two opposite sides, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the total perimeter is 128 feet and one pair of opposite sides (the lengths) are each 47 feet, we can set up the equation as follows:
\[ 128 = 2 \times (47 + \text{width}) \]
First, we simplify inside the parentheses:
\[ 128 = 2 \times (47 + \text{width}) \]
Next, we divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 64 = 47 + \text{width} \]
Now, we solve for the width by subtracting 47 from both sides:
\[ \text{width} = 64 - 47 \]
\[ \text{width} = 17 \]
Thus, the length of the remaining two opposite sides should be 17 feet each.
### 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?
GPT-4o:
To find the length of one side of a square given its perimeter, we use the formula for the perimeter of a square:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 356 meters, we can set up the equation:
\[ 4 \times \text{side length} = 356 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{356}{4} \]
Performing the division:
\[ \text{side length} = 89 \]
### Answer: 89 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides. The lengths of the three known sides are: - First side: 89 units - Second side: 87 units - Third side: 1 unit First, we add these three sides together: \[ 89 + 87 + 1 = 177 \] Next, we subtract this sum from the total perimeter of the quadrilateral to find the length of the fourth side: \[ 236 - 177 = 59 \] Thus, the length of the fourth side is 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?
GPT-4o:
To find the length of each side of the square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 340 meters, we can set up the equation:
\[ 4s = 340 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{340}{4} \]
\[ s = 85 \]
So, the length of each side of the square is 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 16 meters, we can set up the equation:
\[ 4s = 16 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{16}{4} \]
\[ s = 4 \]
So, the length of each side of the square is 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we need to use the information about the perimeter. The perimeter of a quadrilateral is the sum of the lengths of all its sides. Given: - Length of the first side = 1 meter - Length of the second side = 54 meters - Length of the third side = 9 meters - Total perimeter = 81 meters Let the length of the fourth side be \( x \) meters. The equation for the perimeter is: \[ 1 + 54 + 9 + x = 81 \] First, we sum the known side lengths: \[ 1 + 54 + 9 = 64 \] Now, we substitute this sum back into the equation: \[ 64 + x = 81 \] To find \( x \), we subtract 64 from both sides of the equation: \[ x = 81 - 64 \] \[ x = 17 \] Therefore, the length of the fourth side is 17 meters. ### Answer: 17 meters
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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 316 meters, we can set up the equation:
\[ 4s = 316 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{316}{4} \]
Performing the division:
\[ s = 79 \]
Thus, 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 300m. How long is each side of the square?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square, which is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 300 meters, we can set up the equation:
\[ 4 \times \text{side length} = 300 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{300}{4} \]
\[ \text{side length} = 75 \]
### Answer: 75 meters
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?
GPT-4o:
To find the length of the remaining side of the quadrilateral, we need to subtract the sum of the known side lengths from the total perimeter.
First, let's add the lengths of the three known sides:
\[ 19 \, \text{m} + 57 \, \text{m} + 22 \, \text{m} = 98 \, \text{m} \]
Next, we subtract this sum from the total perimeter:
\[ 198 \, \text{m} - 98 \, \text{m} = 100 \, \text{m} \]
Therefore, the length of the remaining side is:
### 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?
GPT-4o:
To find the length of each side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 172 meters, we can set up the equation:
\[ 4s = 172 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{172}{4} \]
\[ s = 43 \]
So, the length of each side of the square is 43 meters.
### Answer: 43 meters
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?
GPT-4o:
To find the length of one side of a square given its perimeter, we can use the formula for the perimeter of a square:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given that the perimeter is 304 cm, we can set up the equation:
\[ 4 \times \text{side length} = 304 \]
To find the side length, we divide both sides of the equation by 4:
\[ \text{side length} = \frac{304}{4} \]
\[ \text{side length} = 76 \]
### 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?
GPT-4o:
To find the length of each of the longer sides of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter is 158 meters and each of the shorter sides (width) is 51 meters, we can set up the equation as follows:
\[ 158 = 2 \times (\text{length} + 51) \]
First, we divide both sides of the equation by 2 to isolate the sum of the length and width:
\[ 79 = \text{length} + 51 \]
Next, we subtract 51 from both sides to solve for the length:
\[ \text{length} = 79 - 51 \]
\[ \text{length} = 28 \]
Therefore, the length of each of the longer sides is 28 meters.
### Answer: 28 meters
Expected answer: 28
Correct? Yes
Problem: A square has a perimeter of 72m. What is the length of one its sides?
GPT-4o:
To find the length of one side of the square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 72 meters, we can set up the equation:
\[ 4s = 72 \]
To find \( s \), we divide both sides of the equation by 4:
\[ s = \frac{72}{4} \]
\[ s = 18 \]
### Answer: 18 meters
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?
GPT-4o:
To find the length of each of the other two sides of the rectangular playground, we start by noting that the total length of the fence is the perimeter of the rectangle. The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{length} + \text{width}) \]
We know the total perimeter is 166 meters, and two of the sides are each 19 meters. Let's denote the unknown length of the other two sides as \( w \) (width).
The perimeter equation can be written as:
\[ 166 = 2 \times (19 + w) \]
First, we simplify the equation:
\[ 166 = 2 \times 19 + 2 \times w \]
\[ 166 = 38 + 2w \]
Next, we isolate \( 2w \) by subtracting 38 from both sides:
\[ 166 - 38 = 2w \]
\[ 128 = 2w \]
Now, we solve for \( w \) by dividing both sides by 2:
\[ w = \frac{128}{2} \]
\[ w = 64 \]
Thus, the length of each of the other two sides is 64 meters.
### Answer: 64 meters
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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides:
\[ 40 \, \text{m} + 32 \, \text{m} + 95 \, \text{m} = 167 \, \text{m} \]
Next, we subtract this sum from the total perimeter of the quadrilateral:
\[ 246 \, \text{m} - 167 \, \text{m} = 79 \, \text{m} \]
Thus, the length of the fourth side is:
### 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?
GPT-4o:
To find the length of one side of a square, we need to use the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side.
Given that the perimeter \( P \) is 32 meters, we can set up the equation:
\[ 4s = 32 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{32}{4} \]
\[ s = 8 \]
### Answer: 8 meters
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?
GPT-4o:
To find the length of one side of the square, we start by using the formula for the perimeter of a square. The perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
Given that the perimeter \( P \) is 12 meters, we can set up the equation:
\[ 4s = 12 \]
To solve for \( s \), we divide both sides of the equation by 4:
\[ s = \frac{12}{4} \]
\[ s = 3 \]
So, the length of one side of the square is 3 meters.
### 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?
GPT-4o:
To find the length of the fourth side of the quadrilateral, we start by adding the lengths of the three known sides:
\[ 29 \, \text{m} + 16 \, \text{m} + 41 \, \text{m} = 86 \, \text{m} \]
Next, we subtract this sum from the total perimeter of the quadrilateral to find the length of the fourth side:
\[ 160 \, \text{m} - 86 \, \text{m} = 74 \, \text{m} \]
### 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?
GPT-4o:
To find the length of the other side of the rectangle, we start by using the formula for the perimeter of a rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
Given that the perimeter is 98 meters and one of the sides (let's call it the width) is 5 meters, we can set up the equation as follows:
\[ 98 = 2 \times (\text{length} + 5) \]
First, divide both sides of the equation by 2 to isolate the sum of the length and the width:
\[ 49 = \text{length} + 5 \]
Next, subtract 5 from both sides to solve for the length:
\[ \text{length} = 49 - 5 \]
\[ \text{length} = 44 \]
Thus, the length of the other side is 44 meters.
### Answer: 44 meters
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?
GPT-4o:
To find the length of each of the other two sides of the rectangle, we start by using the formula for the perimeter of a rectangle. The perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{width}) \]
We know the perimeter \( P \) is 210 meters, and two of the sides (lengths) are each 45 meters. Let's denote the unknown width by \( w \).
First, we can set up the equation for the perimeter:
\[ 210 = 2 \times (45 + w) \]
Next, we solve for \( w \):
1. Divide both sides by 2:
\[ 105 = 45 + w \]
2. Subtract 45 from both sides:
\[ 105 - 45 = w \]
\[ 60 = w \]
So, the length of each of the other two sides (widths) is 60 meters.
### Answer: 60 meters
Expected answer: 60
Correct? Yes