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?

DeepSeek 67B:

Reasoning:
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given the perimeter (P = 324 meters) and the length (L = 83 meters). We need to find the width (W).

Solution:
We can rearrange the formula to solve for W: W = (P/2) - L
Substituting the given values, we get: W = (324/2) - 83
W = 162 - 83
W = 79

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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

Given that the perimeter is 40m, we can set up the equation:

40 = 4s

Now, we can solve for 's':

s = 40 / 4
s = 10

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

Given that the perimeter is 344m, we can set up the equation:

344 = 4s

Now, we can solve for 's':

s = 344 / 4
s = 86

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

Given that the perimeter is 348m, we can write:

348 = 4s

Now, we can solve for 's':

s = 348 / 4
s = 87

So, the length of each side of the square is 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the unknown side as x. The perimeter of a rectangle is given by the formula: 2*(length + width). In this case, the perimeter is 194 cm and the length of one side is 49 cm.

So, we can set up the equation as follows:

2*(49 + x) = 194

Now, we can solve for x:

98 + 2x = 194

Subtract 98 from both sides:

2x = 96

Divide both sides by 2:

x = 48

The length of the other side is 48 cm.

### Answer: 48

Expected answer: 48

Correct? Yes

Problem: A square has a perimeter of 192m. What is the length of one side?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 192m, we can set up the equation:

192 = 4s

Now, we can solve for 's':

s = 192 / 4
s = 48

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 68 cm

s + s + s + s = 68

4s = 68

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 68 / 4

s = 17

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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the rectangle as L and the width as W. The perimeter of a rectangle is given by the formula:

Perimeter = 2L + 2W

We know that the perimeter is 52 meters, and one side (W) is 4 meters. We can substitute these values into the formula:

52 = 2L + 2(4)

Now, we can solve for L:

52 = 2L + 8
44 = 2L
L = 22

So, the length of the rectangle is 22 meters. The other side (W) is already given as 4 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the lengths of the two unknown sides as x and y.
The perimeter of the quadrilateral is given as 229m, so we can write the equation:
93m + 98m + 36m + x + y = 229m
Combining like terms, we get:
227m + x + y = 229m
Subtracting 227m from both sides, we get:
x + y = 2m
Since we are looking for the length of the fourth side, we need to find the value of y.
We know that the third side is 36m long, so we can substitute this value into the equation:
x + 36m = 2m
Subtracting 36m from both sides, we get:
x = -34m
Since the length of a side cannot be negative, there is no solution for the length of the fourth side in this case.
The answer is: 36

Expected answer: 2

Correct? No

Problem: The perimeter of a square is 16m. What is the length of each side of this square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 16m

s + s + s + s = 16m

4s = 16m

To find the length of each side, we divide both sides of the equation by 4:

s = 16m / 4

s = 4m

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 272m

s + s + s + s = 272

4s = 272

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 272 / 4

s = 68

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 244m

s + s + s + s = 244

4s = 244

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 244 / 4

s = 61

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The perimeter of the quadrilateral is 70m + 29m + 61m + x = 227m.

Solution:
70m + 29m + 61m + x = 227m
160m + x = 227m
x = 227m - 160m
x = 67m

The length of the fourth side of the quadrilateral is 67m.
### Answer: 67

Expected answer: 67

Correct? Yes

Problem: A square has a perimeter of 280m. What is the length of the side of that square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 280m

s + s + s + s = 280m

4s = 280m

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 280m / 4

s = 70m

The length of one side of the square 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the lengths of the two known sides as a and b, and the length of the third side as c.
The perimeter of the quadrilateral is given as P = a + b + c + d, where d is the length of the fourth side.
We are given that P = 219cm, a = 37cm, b = 98cm, and c = 41cm.
Substituting these values into the equation, we get:
219 = 37 + 98 + 41 + d
Now, we can solve for d:
219 = 176 + d
d = 219 - 176
d = 43
Therefore, the length of the fourth side is 43cm.
### Answer: 43

Expected answer: 43

Correct? Yes

Problem: A square has a perimeter of 44m. Can you calculate the length of one side?

DeepSeek 67B:

Reasoning:
A square has four equal sides. To find the length of one side, we can divide the perimeter by the number of sides.

Solution:
The length of one side of the square is 44m / 4 = <<44/4=11>>11m.
### 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the shorter side as x. Since the longer side is 71 meters, the total length of the two sides is 71 + x.
The perimeter of a rectangle is calculated by adding all four sides, which in this case is 2 * (length + width).
So, we can write the equation as:
2 * (71 + x) = 282
Let's solve for x:
142 + 2x = 282
To isolate x, we subtract 142 from both sides of the equation:
142 + 2x - 142 = 282 - 142
2x = 140
To solve for x, we divide both sides of the equation by 2:
x = 140 / 2
x = 70
The length of the shorter side 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?

DeepSeek 67B:

Reasoning:
Let's denote the shorter side of the garden as 'a' and the longer side as 'b'. The perimeter of a rectangle is given by the formula: 2*(length + width). In this case, the perimeter is 128 meters, and the shorter side is 57 meters.

So, we can write the equation as:
2*(a + b) = 128

We know that a = 57 meters. Now, we can substitute the value of 'a' into the equation:
2*(57 + b) = 128

Now, we can solve for 'b':
114 + 2b = 128
2b = 128 - 114
2b = 14
b = 14 / 2
b = 7

So, the other side (the longer side) of the garden is 7 meters long.

### 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

We know that the perimeter is 392m.

392 = 4s

Now, we can solve for 's' by dividing both sides of the equation by 4.

s = 392 / 4

s = 98

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the unknown side as x. The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since the rectangle has two pairs of equal sides, we can represent the perimeter as:

2 * length + 2 * width = 204

We know that one of the sides (length) is 16m, so we can substitute that into the equation:

2 * 16 + 2 * x = 204

Now, we can solve for x:

32 + 2x = 204

Subtract 32 from both sides:

2x = 172

Divide both sides by 2:

x = 86

So, the length of the other side (width) is 86m.

Expected answer: 86

Correct? Yes

Problem: A square has a perimeter of 336cm. What is the length of one of its sides?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 336cm, we can set up the equation:

336 = 4s

Now, we can solve for 's':

s = 336 / 4
s = 84

So, the length of one side of the square is 84cm.

### Answer: 84

Expected answer: 84

Correct? Yes

Problem: A square has a perimeter of 144 meters. What is the length of one side of the square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4 * s

Given that the perimeter is 144 meters, we can write:

144 = 4 * s

Now, we can solve for 's':

s = 144 / 4
s = 36

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides. In this case, the perimeter is 236 cm. We know the lengths of three sides, so we can find the length of the fourth side by subtracting the sum of the known side lengths from the perimeter.

Let's denote the lengths of the known sides as a, b, and c, and the length of the unknown side as d. We have:

a = 69 cm
b = 50 cm
c = 39 cm

The perimeter P is given by:

P = a + b + c + d

We can plug in the known values and solve for d:

236 = 69 + 50 + 39 + d

Now, we can simplify and solve for d:

236 = 158 + d

d = 236 - 158

d = 78 cm

So, the length of the fourth side is 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the unknown side as x.
The perimeter of the quadrilateral is 193cm, so we can write the equation:
37cm + 14cm + 73cm + x = 193cm
Let's simplify and solve for x:
124cm + x = 193cm
To isolate x, we subtract 124cm from both sides of the equation:
124cm - 124cm + x = 193cm - 124cm
x = 69cm
The length of the unknown side is 69cm.
### Answer: 69

Expected answer: 69

Correct? Yes

Problem: A square has a perimeter of 160m. What is the length of one of its sides?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4 * s

Given that the perimeter is 160m, we can write:

160 = 4 * s

Now, we can solve for 's':

s = 160 / 4
s = 40

So, 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?

DeepSeek 67B:

Reasoning:
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter is 228 meters and the length is 90 meters. We can substitute these values into the formula and solve for the width.
228 = 2(90) + 2W
228 = 180 + 2W
To isolate W, we subtract 180 from both sides of the equation:
228 - 180 = 180 - 180 + 2W
48 = 2W
To solve for W, we divide both sides of the equation by 2:
48 / 2 = 2W / 2
24 = W
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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides are equal in a square, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 136 meters, we can write:

136 = 4s

Now, we can solve for 's':

s = 136 / 4
s = 34

So, the length of one side of the 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the opposite side as x. Since the rectangle has a total perimeter of 236 meters, we can use the formula for the perimeter of a rectangle:

Perimeter = 2 * (length + width)

In this case, the length is 43 meters and the width is x meters. So, we can write the equation as:

236 = 2 * (43 + x)

Now, we can solve for x:

236 = 86 + 2x

Subtract 86 from both sides:

236 - 86 = 86 - 86 + 2x

150 = 2x

Divide both sides by 2:

150 / 2 = 2x / 2

75 = x

So, the length of the opposite side is 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides. In this case, the perimeter is 206m.
We know that two sides together have a length of 58m, and the other two sides together have a length of 54m and 1m, respectively.
Let's denote the missing side as x.
The sum of the lengths of all four sides is 206m, so we can write the equation as:
58m + 54m + 1m + x = 206m
Let's simplify and solve for x:
113m + x = 206m
To isolate x, we subtract 113m from both sides of the equation:
113m + x - 113m = 206m - 113m
x = 93m
The length of the missing portion of the perimeter is 93m.
### 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is calculated by multiplying the length of one side by 4.
Let's denote the length of one side as "s".
So, the perimeter of the square field is 4s.
We know that the perimeter is 284 meters.
Therefore, 4s = 284.
To find the length of one side, we need to divide both sides of the equation by 4.
s = 284/4.
Calculating the value of s, we get s = 71.
So, 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?

DeepSeek 67B:

Reasoning:
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter is 150 feet and the length is 69 feet.
We can substitute these values into the formula to find the width.
150 = 2(69) + 2W
150 = 138 + 2W
To isolate W, we subtract 138 from both sides of the equation.
150 - 138 = 138 - 138 + 2W
12 = 2W
To solve for W, we divide both sides of the equation by 2.
12/2 = 2W/2
6 = W
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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the rectangle as L and the width as W. The perimeter of a rectangle is given by the formula:

Perimeter = 2(L + W)

We know that the perimeter is 166m, and one side (W) is 35m. We can plug these values into the formula and solve for the other side (L):

166 = 2(L + 35)

Now, we can solve for L:

166 = 2L + 70

Subtract 70 from both sides:

96 = 2L

Divide both sides by 2:

L = 48

So, the other side (L) is 48m.

### Answer: 48

Expected answer: 48

Correct? Yes

Problem: A square has a perimeter of 124m. What is the length of each side?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 124m

s + s + s + s = 124

4s = 124

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 124 / 4

s = 31

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the opposite side as x. Since the field is rectangular, the other two sides have the same length. The perimeter of a rectangle is given by the formula: 2*(length + width). In this case, the perimeter is 336 feet, and the length is 79 feet.

2*(79 + x) = 336

Now, we can solve for x:

158 + 2x = 336
2x = 336 - 158
2x = 178
x = 178 / 2
x = 89

The length of the opposite side 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 132 meters

s + s + s + s = 132

4s = 132

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 132 / 4

s = 33

So, the length of one side of the square is 33 meters.

### Answer: 33

Expected answer: 33

Correct? Yes

Problem: A rectangle has a perimeter of 138 feet. If the length of the rectangle is 46 feet, what is the width of the rectangle?

DeepSeek 67B:

Reasoning:
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter is 138 feet and the length is 46 feet. We can substitute these values into the formula and solve for the width.
138 = 2(46) + 2W
138 = 92 + 2W
46 = 2W
23 = W
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?

DeepSeek 67B:

Reasoning:
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter is 200 meters and the length is 49 meters. We can substitute these values into the formula to find the width.
200 = 2(49) + 2W
200 = 98 + 2W
102 = 2W
W = 102/2
W = 51
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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 200m

Perimeter = 4s

200 = 4s

To find the length of each side, we divide both sides of the equation by 4:

s = 200 / 4

s = 50

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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The perimeter of the quadrilateral is given as 199m.
So, the sum of the lengths of all its sides is 199m.
The length of the first side is 9m, the length of the second side is 30m, and the length of the third side is 71m.
Therefore, the sum of the lengths of the first three sides is 9m + 30m + 71m = 110m.
To find the length of the fourth side, we subtract the sum of the lengths of the first three sides from the perimeter of the quadrilateral.
So, x = 199m - 110m = 89m.
The length of the fourth side is 89m.
### Answer: 89

Expected answer: 89

Correct? Yes

Problem: A quadrilateral has a perimeter of 207m. The lengths of three of its sides are 35m, 62m and 70m respectively. What is the length of the fourth side?

DeepSeek 67B:

Reasoning:
Let's denote the lengths of the three known sides as a, b, and c, and the length of the unknown side as d. We know that a = 35m, b = 62m, and c = 70m. The perimeter of a quadrilateral is the sum of the lengths of all its sides. Therefore, we can write the equation:

a + b + c + d = Perimeter

Substituting the known values, we get:

35 + 62 + 70 + d = 207

Now, we can solve for d:

167 + d = 207

d = 207 - 167

d = 40

The length of the fourth side is 40m.
### Answer: 40

Expected answer: 40

Correct? Yes

Problem: A rectangle has a perimeter of 384cm. If one of the shorter sides of the rectangle is measured to be 99cm, what would be the length of the longer sides of the rectangle?

DeepSeek 67B:

Reasoning:
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, we have P = 384cm and one of the shorter sides (W) is 99cm.
We can rearrange the formula to solve for the length (L): L = (P/2) - W.
Substituting the given values, we get L = (384/2) - 99 = 192 - 99 = 93cm.
Therefore, the length of the longer side of the rectangle is 93cm.
### 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the lengths of the first, second, third, and fourth sides as a, b, c, and d respectively.
We know that a = 78m, b = 15m, and c = 63m.
The perimeter of the quadrilateral is given as 255m.
So, a + b + c + d = 255m.
Substituting the known values, we get:
78m + 15m + 63m + d = 255m.
Combining like terms, we get:
156m + d = 255m.
Subtracting 156m from both sides, we get:
d = 255m - 156m.
d = 99m.
Therefore, the length of the fourth side is 99m.
### Answer: 99

Expected answer: 99

Correct? Yes

Problem: A square has a perimeter of 128m. What is the length of one of its sides?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4 * s

Given that the perimeter is 128m, we can write:

128 = 4 * s

Now, we can solve for 's':

s = 128 / 4
s = 32

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the other pair of opposite sides as x. Since the perimeter of a rectangle is given by the formula P = 2(length + width), we can write the equation as follows:

96 = 2(33 + x)

Now, we can solve for x:

96 = 66 + 2x
2x = 96 - 66
2x = 30
x = 30 / 2
x = 15

So, the length of the other pair of opposite sides 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side.

Let's calculate the length of each side:

Perimeter = 112 meters
Length of each side = Perimeter / 4
Length of each side = 112 / 4
Length of each side = 28 meters

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since all sides of a square are equal in length, we can find the length of one side by dividing the perimeter by the number of sides.

Solution:
The perimeter of the square is 32 cm.
Since a square has 4 sides, we can divide the perimeter by 4 to find the length of one side.
32 cm / 4 = 8 cm

Answer: The length of one side of the square is 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

Given that the perimeter is 364m, we can set up the equation:

364 = 4s

Now, we can solve for 's':

s = 364 / 4
s = 91

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the other side as x. The perimeter of a rectangle is given by the formula: 2*(length + width). In this case, the perimeter is 144 feet and the length is 38 feet.

So, we can write the equation as:
2*(38 + x) = 144

Now, we can solve for x:
76 + 2x = 144
2x = 144 - 76
2x = 68
x = 68/2
x = 34

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?

DeepSeek 67B:

Reasoning:
Let's denote the sides of the quadrilateral as a, b, c, and d. We know that a + b = 54m, c = 22m, and d = 37m. The perimeter of the quadrilateral is given by the formula:

Perimeter = a + b + c + d

We can substitute the given values into the formula:

205m = 54m + c + d

Now, we can substitute the values of c and d:

205m = 54m + 22m + 37m

Now, we can solve for the remaining side (a + b):

205m = 113m

To find the length of the remaining side, we subtract the sum of the known sides from the perimeter:

a + b = 205m - 113m = 92m

So, the length of the remaining side is 92m.

Expected answer: 92

Correct? Yes

Problem: The perimeter of a rectangular field is 174m. If the length of the field is 65m, what is the width of the field?

DeepSeek 67B:

Reasoning:
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter is 174m and the length is 65m. We can substitute these values into the formula to find the width.
174 = 2(65) + 2W
174 = 130 + 2W
To isolate W, we subtract 130 from both sides of the equation.
174 - 130 = 130 - 130 + 2W
44 = 2W
To solve for W, we divide both sides of the equation by 2.
44 / 2 = 2W / 2
22 = W
The width of the field is 22m.
### Answer: 22

Expected answer: 22

Correct? Yes

Problem: A quadrilateral has a perimeter of 176 cm. The lengths of three sides are 25 cm, 17 cm and 89 cm respectively. What is the length of the fourth side?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The perimeter of the quadrilateral is given as 176 cm, so we can write the equation:
25 + 17 + 89 + x = 176

Solving the equation:
131 + x = 176
x = 176 - 131
x = 45

The length of the fourth side 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

We know that the perimeter is 372 meters.

372 = 4s

Now, we can solve for 's' by dividing both sides of the equation by 4.

s = 372 / 4

s = 93

So, the length of each side of the square is 93 meters.

### Answer: 93

Expected answer: 93

Correct? Yes

Problem: A square field has a perimeter of 240 meters. Can you find out the length of one side of the field?

DeepSeek 67B:

Reasoning:
A square has four equal sides. To find the length of one side, we can divide the perimeter by the number of sides.

Let's denote the length of one side as 's'.

Perimeter = 240 meters
Number of sides = 4

Perimeter = s * 4

Now, we can solve for 's':

240 = s * 4

Divide both sides by 4:

s = 240 / 4

s = 60

So, the length of one side of the 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the other side as x. The perimeter of a rectangle is given by the formula: 2*(length + width). In this case, the perimeter is 242 meters, and one side is 97 meters.

2*(97 + x) = 242

Solving for x:

194 + 2x = 242
2x = 242 - 194
2x = 48
x = 48 / 2
x = 24

The length of the other side is 24 meters.
### Answer: 24

Expected answer: 24

Correct? Yes

Problem: Tom has constructed a square with a total perimeter of 316 meters. Can you determine the length of each side of this square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is calculated by multiplying the length of one side by 4. So, if we let x be the length of one side of the square, we can write the equation:

4x = 316

Now, we can solve for x by dividing both sides of the equation by 4:

x = 316 / 4

x = 79

So, 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 268cm. What is the length of each side of the square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 268 cm

s + s + s + s = 268

4s = 268

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 268 / 4

s = 67

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

We know that the perimeter is 348m.

348 = 4s

Now, we can solve for 's' by dividing both sides of the equation by 4.

s = 348 / 4

s = 87

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 400m, we can write:

400 = 4s

Now, we can solve for 's':

s = 400 / 4
s = 100

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the fourth side as x.
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
So, the perimeter of this quadrilateral is 81m + 100m + 19m + x = 243m.

Solution:
81m + 100m + 19m + x = 243m
200m + x = 243m
To isolate x, we subtract 200m from both sides of the equation:
200m + x - 200m = 243m - 200m
x = 43m
The length of the fourth side 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the unknown side as x. The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is 186cm, and we know that one side is 50cm long. Therefore, the other three sides have a combined length of 186 - 50 = 136cm.

Since the rectangle has two pairs of equal sides, the unknown side (x) and the other known side (50cm) form one pair, and the other pair has a combined length of 136 - 50 = 86cm.

Since the other pair of sides is equal, we can divide the combined length of 86cm by 2 to find the length of one side: 86 / 2 = 43cm.

So, the other side of the rectangle is 43cm 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the adjacent side as x. The perimeter of a rectangle is given by the formula: 2*(length + width). In this case, the perimeter is 224 cm and the length of one side is 78 cm.

2*(78 + x) = 224

Solving for x:

156 + 2x = 224
2x = 224 - 156
2x = 68
x = 68 / 2
x = 34

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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the fourth side as x.
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
So, the perimeter of this quadrilateral is 79m + 97m + 51m + x = 235m.

Solution:
79m + 97m + 51m + x = 235m
227m + x = 235m
x = 235m - 227m
x = 8m

The length of the fourth side is 8m.

Expected answer: 8

Correct? Yes

Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is calculated by multiplying the length of one side by 4. Therefore, to find the length of one side, we can divide the perimeter by 4.

Let's calculate the length of one side of the square:

Length of one side = Perimeter / 4
Length of one side = 28m / 4
Length of one side = 7m

### Answer: 7

Expected answer: 7

Correct? Yes

Problem: A square has a perimeter of 48cm. What is the length of each side?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

Given that the perimeter is 48cm, we can set up the equation:

4s = 48

Now, we can solve for 's':

s = 48 / 4
s = 12

So, the length of each side of the square is 12cm.

### 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?

DeepSeek 67B:

Reasoning:
A square has all sides equal in length. The perimeter of a square is calculated by adding the lengths of all four sides.

Let's denote the length of one side of the square as 's'.

The perimeter of the square is given by the formula:

Perimeter = 4 × side length

In this case, the perimeter is 184 meters. So, we can write the equation as:

184 = 4 × s

Now, we need to solve for 's'.

Divide both sides of the equation by 4:

184 � 4 = s

s = 46

So, the length of one side of the plot 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 56 meters

s + s + s + s = 56

4s = 56

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 56 / 4

s = 14

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The perimeter of the quadrilateral is given as 157m.
So, the sum of the lengths of all its sides is 157m.
We know the lengths of three sides: 97m, 5m, and 30m.
Therefore, the sum of the lengths of these three sides is 97m + 5m + 30m = 132m.
To find the length of the fourth side, we subtract the sum of the lengths of the known sides from the perimeter:
157m - 132m = 25m.
So, the length of the fourth side is 25m.
### Answer: 25

Expected answer: 25

Correct? Yes

Problem: A quadrilateral has a perimeter of 173m. The length of the first side is 46m, second side is 50m and third side is 35m. What is the length of the fourth side?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The perimeter of the quadrilateral is given as 173m.
So, the sum of the lengths of all its sides is 173m.
The length of the first side is 46m, the second side is 50m, and the third side is 35m.
Therefore, the sum of the lengths of the first three sides is 46m + 50m + 35m = 131m.
To find the length of the fourth side, we subtract the sum of the lengths of the first three sides from the perimeter of the quadrilateral.
So, x = 173m - 131m = 42m.
The length of the fourth side is 42m.
### Answer: 42

Expected answer: 42

Correct? Yes

Problem: A square has a perimeter of 72 cm. What is the length of one of its sides?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 72 cm, we can set up the equation:

72 = 4s

Now, we can solve for 's':

s = 72 / 4
s = 18

So, the length of one side of the square is 18 cm.

### Answer: 18

Expected answer: 18

Correct? Yes

Problem: A square has a perimeter of 352m. What is the length of each side of the square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

We know that the perimeter is 352m.

352 = 4s

Now, we can solve for 's' by dividing both sides of the equation by 4.

s = 352 / 4

s = 88

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the width of the rectangle as w. The perimeter of a rectangle is given by the formula: 2*(length + width).

We know the length of the rectangle is 23m and the total perimeter is 116m. We can substitute these values into the formula to find the width:

2*(23 + w) = 116

Now, we can solve for w:

46 + 2w = 116
2w = 116 - 46
2w = 70
w = 70 / 2
w = 35

The length of the width is 35m.
### Answer: 35

Expected answer: 35

Correct? Yes

Problem: A square has a perimeter of 124m. What is the length of each side?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 124m

s + s + s + s = 124

4s = 124

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 124 / 4

s = 31

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the fourth side as x. Since the quadrilateral has a total perimeter of 131m, the sum of the lengths of all four sides should be equal to 131m.

So, we can write the equation as:

24m + 57m + 17m + x = 131m

Now, we can solve for x:

x = 131m - (24m + 57m + 17m)
x = 131m - 98m
x = 33m

The length of the fourth side is 33m.

### 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the unknown side as x. The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since the rectangle has two pairs of equal sides, we can represent the perimeter as:

2 * length + 2 * width = 254

We know that one of the sides has a length of 89m, so we can substitute that into the equation:

2 * 89 + 2 * x = 254

Now, we can solve for x:

178 + 2x = 254

Subtract 178 from both sides:

2x = 76

Divide both sides by 2:

x = 38

So, the length of the other side is 38m.

Expected answer: 38

Correct? Yes

Problem: A square has a perimeter of 208m. What is the length of each side?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 208m

s + s + s + s = 208

4s = 208

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 208 / 4

s = 52

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 64m

s + s + s + s = 64

4s = 64

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 64 / 4

s = 16

So, 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?

DeepSeek 67B:

Reasoning:
The total perimeter of the quadrilateral is 196 meters. The sum of the lengths of three sides is 183 meters. Therefore, the length of the fourth side can be found by subtracting the sum of the lengths of the three known sides from the total perimeter.

Solution:
Length of the fourth side = Total perimeter - Sum of lengths of three known sides
Length of the fourth side = 196 - 183
Length of the fourth side = 13 meters

The length of the fourth side is 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The perimeter of the quadrilateral is given as 191 units.
So, the sum of the lengths of all its sides is 191 units.
The sum of the lengths of the first three sides is 35 + 76 + 5 = 116 units.
Therefore, the length of the fourth side is 191 - 116 = 75 units.
### Answer: 75

Expected answer: 75

Correct? Yes

Problem: A square has a perimeter of 104m. What is the length of each side?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all four sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 104m

s + s + s + s = 104

4s = 104

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 104 / 4

s = 26

So, 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?

DeepSeek 67B:

Reasoning:
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter is 198 cm and the length is 90 cm. We can substitute these values into the formula and solve for the width.
198 = 2(90) + 2W
198 = 180 + 2W
To isolate W, we subtract 180 from both sides of the equation:
198 - 180 = 180 - 180 + 2W
18 = 2W
To solve for W, we divide both sides of the equation by 2:
18 / 2 = 2W / 2
9 = W
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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the remaining two opposite sides as x. Since the total perimeter is 128 feet, we can write the equation:

2(47) + 2x = 128

Solving for x:

94 + 2x = 128
2x = 128 - 94
2x = 34
x = 34 / 2
x = 17

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

We are given that the perimeter is 356m.

356 = 4s

Now, we can solve for 's' by dividing both sides of the equation by 4.

s = 356 / 4

s = 89

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the fourth side as x.
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
So, we can write the equation as:
89 + 87 + 1 + x = 236

Solving the equation:
x = 236 - (89 + 87 + 1)
x = 236 - 177
x = 59

The length of the fourth side is 59 units.
### Answer: 59

Expected answer: 59

Correct? Yes

Problem: A square has a perimeter of 340 meters. What is the length of each side of this square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

We know that the perimeter is 340 meters.

340 = 4s

Now, we can solve for 's' by dividing both sides of the equation by 4.

s = 340 / 4

s = 85

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of all its sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 16m

s + s + s + s = 16m

4s = 16m

To find the length of each side, we divide both sides of the equation by 4:

s = 16m / 4

s = 4m

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The total perimeter of the quadrilateral is 81m, so we can write the equation as:
1m + 54m + 9m + x = 81m

Solving the equation:
74m + x = 81m
x = 81m - 74m
x = 7m

The length of the fourth side is 7 meters.

Expected answer: 17

Correct? No

Problem: A quadrilateral, which is a perfect square, has a total perimeter of 316m. What is the length of each side of this square?

DeepSeek 67B:

Reasoning:
A square has four equal sides. If we divide the total perimeter by 4, we will get the length of each side.

Solution:
The length of each side of the square is 316m / 4 = <<316/4=79>>79m.
### Answer: 79

Expected answer: 79

Correct? Yes

Problem: A square has a perimeter of 300m. How long is each side of the square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 4s

Given that the perimeter is 300m, we can write:

300 = 4s

Now, we can solve for 's':

s = 300 / 4
s = 75

So, each side of the square is 75 meters long.

### 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?

DeepSeek 67B:

Reasoning:
Let's denote the lengths of the two known sides as a and b, and the length of the unknown side as c. The perimeter of a quadrilateral is the sum of the lengths of all its sides.

Perimeter = a + b + c + d

We are given the perimeter (198m) and the lengths of two sides (19m and 57m). We can also assume that the length of the third side is 22m.

198 = 19 + 57 + 22 + c

Now, we can solve for c:

198 = 98 + c
c = 198 - 98
c = 100

The length of the remaining side is 100m.

Expected answer: 100

Correct? Yes

Problem: A square has a perimeter of 172m. What is the length of each side of the square?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's denote the length of each side as 's'.

Perimeter = 172m

s + s + s + s = 172m

4s = 172m

Now, we can solve for 's' by dividing both sides of the equation by 4:

s = 172m / 4

s = 43m

So, 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?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 304 cm, we can set up the equation:

304 = 4s

Now, we can solve for 's':

s = 304 / 4
s = 76

So, 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the shorter sides as 'a' and the length of the longer sides as 'b'. We know that the total perimeter of a rectangle is given by the formula: 2*(length + width).

In this case, we have:
2*(a + b) = 158

We also know that each of the shorter sides is 51 meters long, so:
a = 51

Now we can substitute the value of 'a' into the formula:
2*(51 + b) = 158

Let's solve for 'b':
102 + 2b = 158
2b = 158 - 102
2b = 56
b = 56 / 2
b = 28

So, the length of each of the longer sides is 28 meters.
### Answer: 28

Expected answer: 28

Correct? Yes

Problem: A square has a perimeter of 72m. What is the length of one its sides?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 72m, we can write:

72 = 4s

Now, we can solve for 's':

s = 72 / 4
s = 18

So, the length of one side of the square is 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the two sides that are 19m each as A and B, and the length of the other two sides as C and D. We know that A = B = 19m.

The total length of the fence is the sum of all four sides, so we have:

A + B + C + D = 166

Substituting A and B with 19m, we get:

19 + 19 + C + D = 166

Combining like terms, we have:

38 + C + D = 166

Now, we need to find the length of C and D. To do this, we can subtract 38 from both sides of the equation:

C + D = 166 - 38

C + D = 128

Since C and D are the lengths of the other two sides of the rectangle, they must be equal. Therefore, we can divide the sum by 2 to find the length of each side:

C = D = 128 / 2

C = D = 64

So, the length of each of the other two sides is 64m.

Expected answer: 64

Correct? Yes

Problem: A quadrilateral has a perimeter of 246m. You know that two of its sides are 40m and 32m long, another side is 95m long. What is the length of the fourth side?

DeepSeek 67B:

Reasoning:
The perimeter of a quadrilateral is the sum of the lengths of all its sides.
Let's denote the length of the fourth side as x.
The perimeter of the quadrilateral is given as 246m.
So, the sum of the lengths of all its sides is 246m.
We know the lengths of three sides: 40m, 32m, and 95m.
Therefore, the sum of the lengths of these three sides is 40m + 32m + 95m = 167m.
To find the length of the fourth side, we subtract the sum of the lengths of the known sides from the perimeter of the quadrilateral:
246m - 167m = 79m.
So, the length of the fourth side is 79m.
### Answer: 79

Expected answer: 79

Correct? Yes

Problem: A square has a perimeter of 32m. What is the length of one of its sides?

DeepSeek 67B:

Reasoning:
The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.

Let's denote the length of one side as 's'.

Perimeter = 4s

Given that the perimeter is 32m, we can set up the equation:

32 = 4s

Now, we can solve for 's':

s = 32 / 4
s = 8

So, 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?

DeepSeek 67B:

Reasoning:
A square has four equal sides. To find the length of one side, we can divide the perimeter by the number of sides.

Solution:
The perimeter of the square is 12 meters.
Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side.
12 meters / 4 = 3 meters

Answer: The length of one side of the square is 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?

DeepSeek 67B:

Reasoning:
Let's denote the lengths of the three known sides as a, b, and c, and the length of the unknown side as d. We know that a = 29m, b = 16m, and c = 41m. The perimeter of a quadrilateral is the sum of the lengths of all its sides. Therefore, we can write the equation:

a + b + c + d = Perimeter

Substituting the known values, we get:

29 + 16 + 41 + d = 160

Now, we can solve for d:

d = 160 - (29 + 16 + 41)
d = 160 - 86
d = 74

So, the length of the fourth side (d) is 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?

DeepSeek 67B:

Reasoning:
Let's denote the length of the unknown side as x. The perimeter of a rectangle is given by the formula: 2*(length + width). In this case, the perimeter is 98m and one side is 5m long.

So, we can write the equation as:
2*(5 + x) = 98

Now, we can solve for x:
10 + 2x = 98
2x = 88
x = 44

The length of the other side is 44m.
### 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?

DeepSeek 67B:

Reasoning:
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We know that two sides of the rectangle measure 45m each, so the total length of these two sides is 2 * 45 = 90m.
We also know that the total perimeter of the rectangle is 210m.
So, we can set up the equation 210 = 2L + 2W, where L and W are the lengths of the other two sides.
We can substitute the known values into the equation: 210 = 2L + 2(90).
Simplifying the equation, we get 210 = 2L + 180.
Subtracting 180 from both sides, we get 30 = 2L.
Dividing both sides by 2, we get L = 15.
So, each of the other two sides of the rectangle measures 15m.
### Answer: 15

Expected answer: 60

Correct? No