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Gemini-1.5 Flash 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

Problem: The perimeter of a rectangular swimming pool is 324 meters. The length of the pool is 83 meters. What is the width of the pool?

Gemini-1.5 Flash:

Reasoning:  The perimeter of a rectangle is calculated by the formula:  Perimeter = 2 * (length + width) We know the perimeter is 324 meters and the length is 83 meters. Let's plug these values into the formula and solve for the width:

324 = 2 * (83 + width)

324 = 166 + 2 * width

324 - 166 = 2 * width

158 = 2 * width

width = 158 / 2

width = 79 meters

### Answer: 79 meters 

Expected answer: 79

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 40m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  If the perimeter is 40m, then each side is 40m / 4 = 10m.

### Answer: 10m 

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 344m. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning: The perimeter of a square is the total length of all its sides. Since a square has four equal sides, we can find the length of one side by dividing the perimeter by 4. 
Therefore, the length of each side is 344m / 4 = <<344/4=86>>86m. 

### Answer: 86m 

Expected answer: 86

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 348m. What would be the length of each side of the square?

Gemini-1.5 Flash:

Reasoning:  A square has four equal sides.  The perimeter is the total length of all the sides added together.  Therefore, to find the length of one side, we can divide the perimeter by 4. 
 
 348m / 4 = <<348/4=87>> 87m

### Answer: 87m 

Expected answer: 87

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 194 cm. The length of one of its sides is 49 cm. Can you determine the length of its other side?

Gemini-1.5 Flash:

Here's how to determine the length of the other side:

1. **Perimeter Formula:** The perimeter of a rectangle is calculated by adding up the lengths of all its sides. The formula is: Perimeter = 2 * (length + width)

2. **We know:**
   - Perimeter = 194 cm
   - Length = 49 cm

3. **Let's substitute the known values into the formula:**
   194 = 2 * (49 + width)

4. **Solve for the width:**
   - 194 = 98 + 2 * width
   - 194 - 98 = 2 * width
   - 96 = 2 * width
   - width = 96 / 2 
   - width = 48 cm

### Answer: 48 cm 

Expected answer: 48

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  To find the length of one side, we divide the perimeter by 4. 
So, the length of one side is 192m / 4 = 48m.
### Answer: 48m 

Expected answer: 48

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 68cm. What is the length of one side?

Gemini-1.5 Flash:

Reasoning:  A square has four equal sides. If the perimeter is 68cm, then each side is 68cm / 4 = 17cm long.

### Answer: 17cm 

Expected answer: 17

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 52 meters. If one of the sides measures 4 meters, how long is the other side?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Perimeter Formula:** The perimeter of a rectangle is calculated by adding up the lengths of all its sides.  The formula is: Perimeter = 2 * (length + width)

2. **Knowns:** We know the perimeter is 52 meters and one side (let's call it the width) is 4 meters.

3. **Substitute:**  Let's plug the known values into the formula: 52 = 2 * (length + 4)

4. **Solve for Length:**
   *  52 = 2 * length + 8
   *  52 - 8 = 2 * length
   *  44 = 2 * length
   *  length = 44 / 2
   *  length = 22 meters

### Answer: 22 meters 

Expected answer: 22

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 229m. Two sides of the quadrilateral have lengths of 93m and 98m respectively. The third side of the quadrilateral is 36m long. What is the length of the fourth side?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Add the known side lengths:** 93m + 98m + 36m = 227m
2. **Subtract the sum of known sides from the perimeter:** 229m - 227m = 2m

**Therefore, the length of the fourth side is 2m.**

### Answer: 2m 

Expected answer: 2

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: The perimeter of a square is the total length of all its sides. Since a square has 4 equal sides, we can find the length of one side by dividing the perimeter by 4. 
Therefore, the length of each side is 16m/4 = 4m.

### Answer: 4m 

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 272m. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning: The perimeter of a square is the total length of all its sides. Since a square has 4 equal sides, we can find the length of one side by dividing the perimeter by 4.  

Therefore, the length of one side is 272m / 4 = <<272/4=68>>68m.

### Answer: 68m 

Expected answer: 68

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 244m. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning: A square has four equal sides. The perimeter is the total length of all sides added together. So, to find the length of one side, we divide the perimeter by 4. 
Therefore, each side of the square is 244/4 = <<244/4=61>>61 meters long.
### Answer: 61 meters. 

Expected answer: 61

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 227m. The lengths of three of its sides are 70m, 29m, and 61m. What is the length of the fourth side of the quadrilateral?

Gemini-1.5 Flash:

Reasoning: The sum of the lengths of the three known sides is 70m + 29m + 61m = 160m. 
The length of the fourth side is equal to the perimeter minus the sum of the lengths of the other three sides: 227m - 160m = 67m.

### Answer: 67m

Expected answer: 67

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  If the perimeter is 280m, then each side is 280m / 4 = 70m. 
### Answer: 70m 

Expected answer: 70

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 219cm. Two of its sides have lengths of 37cm and 98cm, and a third side is known to be 41cm. How long is the fourth side?

Gemini-1.5 Flash:

Reasoning:  The perimeter of a quadrilateral is the sum of all its sides. We know three sides of the quadrilateral: 37cm, 98cm, and 41cm.  

First, we add the lengths of the three known sides: 37cm + 98cm + 41cm = 176cm.

Then, we subtract the sum of the three known sides from the total perimeter to find the length of the fourth side: 219cm - 176cm = 43cm.

### Answer: 43cm 

Expected answer: 43

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Here's how to calculate the length of one side:

* **Perimeter of a square:** The perimeter of a square is the total length of all its sides added together.
* **Formula:**  Perimeter = 4 * side
* **Given:** Perimeter = 44m

Now, we can solve for the side:

1. **Substitute:** 44 = 4 * side
2. **Divide both sides by 4:** 44/4 = side
3. **Calculate:** 11 = side

Therefore, the length of one side of the square is 11 meters.

### Answer: 11m 

Expected answer: 11

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a perimeter of 282 meters. The longer side measures 71 meters. What is the length of the shorter side?

Gemini-1.5 Flash:

Reasoning: 
1. We know that the perimeter of a rectangle is calculated by adding up the lengths of all its sides: Perimeter = 2 * (length + width).
2. We are given the perimeter (282 meters) and the length (71 meters). 
3. Let's substitute these values into the formula: 282 = 2 * (71 + width).
4. Simplifying the equation: 282 = 142 + 2 * width.
5. Subtracting 142 from both sides: 282 - 142 = 2 * width.
6. This gives us: 140 = 2 * width.
7. Dividing both sides by 2: 140 / 2 = width.
8. Therefore, the width (shorter side) is 70 meters.

### Answer: 70 meters 

Expected answer: 70

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a total perimeter of 128 meters. If the shorter side of the garden has a length of 57 meters, how long is the other side?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Perimeter Formula:** The perimeter of a rectangle is calculated by adding up the lengths of all four sides: Perimeter = 2 * (length + width)
2. **We know:**
    * Perimeter = 128 meters
    * Short side (width) = 57 meters
3. **Let's find the length:**
    * 128 = 2 * (length + 57)
    * 128 = 2 * length + 114
    * 128 - 114 = 2 * length
    * 14 = 2 * length
    * length = 14 / 2
    * length = 7 meters

### Answer: 7 

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 392m. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  To find the length of one side, we divide the perimeter by 4. 
 
The length of each side is 392m / 4 = 98m

### Answer: 98m 

Expected answer: 98

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 204m. If one of its sides has a length of 16m, what is the length of the other side?

Gemini-1.5 Flash:

Here's how to solve this:

1. **Perimeter Formula:** The perimeter of a rectangle is calculated by adding up the lengths of all its sides: Perimeter = 2 * (length + width)

2. **Given Information:** We know the perimeter (204m) and one side (16m). 

3. **Let's represent the unknown side:** Let 'w' be the length of the other side (width).

4. **Plug in the values:** 204 = 2 * (16 + w)

5. **Solve for 'w':**
   * 204 = 32 + 2w
   * 172 = 2w
   * w = 86

Therefore, the length of the other side (width) is 86 meters.

### Answer: 86 

Expected answer: 86

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides. If the perimeter is 336 cm, then each side is 336/4 = 84 cm long. 
### Answer: 84 cm 

Expected answer: 84

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  The perimeter of the square is the total length of all four sides. To find the length of one side, we divide the perimeter by 4.  Therefore, the length of one side is 144 meters / 4 = 36 meters. 
### Answer: 36 meters 

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 236 cm. Two of its sides measure 69 cm and 50 cm respectively, and a third side measures 39 cm. What is the length of the fourth side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of all its sides. So, we can find the length of the fourth side by subtracting the lengths of the other three sides from the total perimeter.

The total length of the three known sides is 69 cm + 50 cm + 39 cm = 158 cm.

The length of the fourth side is 236 cm - 158 cm = 78 cm.

### Answer: 78 cm

Expected answer: 78

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 193cm. Two of its sides measure 37cm and 14cm, while the other two sides measure 73cm and an unknown length. What is the length of the side of the quadrilateral that is unknown?

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of all its sides. We know the lengths of three sides: 37cm, 14cm, and 73cm. The sum of these three sides is 37+14+73 = 124cm. The perimeter of the quadrilateral is 193cm, so the unknown side length is 193-124 = 69cm.
### Answer: 69cm 

Expected answer: 69

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides. Therefore, to find the length of one side, we divide the perimeter by 4: 160m / 4 = 40m.

### Answer: 40m 

Expected answer: 40

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 228 meters. The length of the rectangle is 90 meters. What is the width of the rectangle?

Gemini-1.5 Flash:

Here's how to find the width of the rectangle:

1. **Recall the perimeter formula:** The perimeter of a rectangle is calculated by adding up the lengths of all its sides: Perimeter = 2 * (length + width).

2. **Plug in the known values:** We know the perimeter (228 meters) and the length (90 meters). Let 'w' represent the width. So, the equation becomes: 228 = 2 * (90 + w)

3. **Simplify the equation:**  228 = 180 + 2w

4. **Solve for 'w':**
   * Subtract 180 from both sides: 228 - 180 = 2w
   * This simplifies to: 48 = 2w
   * Divide both sides by 2: 48 / 2 = w

5. **The answer:** w = 24

### Answer: 24 meters 

Expected answer: 24

Correct? Yes

🔗 Problem

Problem: The perimeter of a square field is 136 meters. Given that all sides are equal in a square, What is the length of one side of the field?

Gemini-1.5 Flash:

Reasoning:  The perimeter of a square is the sum of all its sides. Since a square has 4 equal sides, we can find the length of one side by dividing the perimeter by 4. 
Therefore, the length of one side is 136 meters / 4 = 34 meters.
### Answer: 34 meters 

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A rectangle has a total perimeter of 236 meters. If one side of the rectangle is 43 meters, can you determine the length of the opposite side?

Gemini-1.5 Flash:

Reasoning: A rectangle has two pairs of equal sides. Since we know one side is 43 meters, the opposite side must also be 43 meters long. 

### Answer: 43 meters 

Expected answer: 75

Correct? No

🔗 Problem

Problem: A quadrilateral has a perimeter of 206m. Two of its sides together have a length of 58m, and the other two sides together have a length of 54m and 1m, respectively. What is the length of the missing portion of the perimeter?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Combine known lengths:** The two sides with lengths 54m and 1m together have a length of 54m + 1m = 55m.

2. **Add known lengths:** The total length of the three known sides is 58m + 55m = 113m.

3. **Subtract from the perimeter:** To find the missing length, subtract the known length from the perimeter: 206m - 113m = 93m.

### Answer: 93m 

Expected answer: 93

Correct? Yes

🔗 Problem

Problem: A square field has a total perimeter of 284 meters. How long is each side of the square field?

Gemini-1.5 Flash:

Reasoning: A square has 4 equal sides. Therefore, the length of one side is equal to the total perimeter divided by 4. 
The length of one side is 284/4 = <<284/4=71>>71 meters.
### Answer: 71 meters 

Expected answer: 71

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 150 feet. If the length of the rectangle is 69 feet, what is the width of the rectangle?

Gemini-1.5 Flash:

Here's how to solve this problem:

**1. Understand the Formula:**

* The perimeter of a rectangle is calculated by: Perimeter = 2 * (length + width)

**2. Set Up the Equation:**

* We know the perimeter (150 feet) and the length (69 feet).  Let 'w' represent the width.  We can plug these values into the formula:
   150 = 2 * (69 + w)

**3. Solve for the Width:**

* Simplify the equation: 150 = 138 + 2w
* Subtract 138 from both sides: 12 = 2w
* Divide both sides by 2: w = 6

**4. Answer:**

### Answer: 6 feet 

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: The perimeter of a rectangle is 166m. If one of the sides measures 35m, how long is the other side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a rectangle is the sum of all its sides, which is twice the length plus twice the width. We know one side is 35m, and the perimeter is 166m. 
 
 Let's represent the unknown side as 'x'.  So:

 2 * 35m + 2 * x = 166m
 70m + 2x = 166m
 2x = 166m - 70m
 2x = 96m
 x = 96m / 2
 x = 48m

Therefore, the other side is 48 meters long.

### Answer: 48m 

Expected answer: 48

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning:  A square has four equal sides.  The perimeter is the total length of all the sides.  To find the length of one side, we divide the perimeter by 4. 

Therefore, the length of each side is 124m / 4 = 31m.

### Answer: 31m 

Expected answer: 31

Correct? Yes

🔗 Problem

Problem: A rectangular field has a perimeter of 336 feet. The length of one of its sides is 79 feet. What is the length of the opposite side?

Gemini-1.5 Flash:

Reasoning: A rectangle has two pairs of sides with equal lengths.  The opposite side of the field will have the same length as the given side. 

### Answer: 79 feet 

Expected answer: 89

Correct? No

🔗 Problem

Problem: A square plot of land has a perimeter of 132 meters. What is the length of one side of the square?

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  The perimeter of a square is the total length of all its sides. To find the length of one side, we divide the perimeter by the number of sides: 132 meters / 4 sides = 33 meters per side.

### Answer: 33 meters 

Expected answer: 33

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Here's how to solve the problem:

* **Perimeter formula:** The perimeter of a rectangle is calculated by adding up the lengths of all its sides: Perimeter = 2 * (length + width)
* **We know:** 
    * Perimeter = 138 feet
    * Length = 46 feet
* **Let's use the formula to find the width:**
    * 138 = 2 * (46 + width)
    * 138 = 92 + 2 * width
    * 138 - 92 = 2 * width
    * 46 = 2 * width
    * width = 46 / 2 
    * width = 23 feet

### Answer: 23 feet 

Expected answer: 23

Correct? Yes

🔗 Problem

Problem: A rectangular field has a total perimeter of 200 meters. The length of the field is known to be 49 meters. What is the width of the field in meters?

Gemini-1.5 Flash:

Here's how to find the width of the field:

* **Perimeter Formula:** The perimeter of a rectangle is calculated by:  Perimeter = 2 * (length + width)
* **We know:**
    * Perimeter = 200 meters
    * Length = 49 meters
* **Substitute and solve for width:**
    * 200 = 2 * (49 + width)
    * 200 = 98 + 2 * width
    * 102 = 2 * width
    * width = 102 / 2 = 51 meters

### Answer: 51 

Expected answer: 51

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 200m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  Therefore, to find the length of one side, we divide the perimeter by 4.  The length of one side is 200m/4 = <<200/4=50>>50m.

### Answer: 50m 

Expected answer: 50

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 199m. The length of one side is 9m, the length of the second side is 30m, and the length of the third side is 71m. What is the length of the fourth side?

Gemini-1.5 Flash:

Reasoning:  The perimeter of a quadrilateral is the sum of the lengths of all its sides. We know the lengths of three sides: 9m, 30m, and 71m.  To find the length of the fourth side, we subtract the sum of the lengths of the known sides from the total perimeter.

* Sum of the known sides: 9m + 30m + 71m = 110m
* Length of the fourth side: 199m - 110m = 89m

### Answer: 89m 

Expected answer: 89

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides.  We know the lengths of three sides, so to find the length of the fourth side, we subtract the sum of the three known sides from the total perimeter. 

The sum of the three known sides is 35m + 62m + 70m = 167m.

Therefore, the length of the fourth side is 207m - 167m = 40m.

### Answer: 40m 

Expected answer: 40

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: 
We know that the perimeter of a rectangle is calculated by: Perimeter = 2 * (length + width)
We are given the perimeter (384 cm) and the width (99 cm).  Let's represent the length as 'l'. 
So, we can plug in the values and solve for 'l':
384 = 2 * (l + 99)
192 = l + 99
l = 192 - 99
l = 93 cm

### Answer: 93 cm 

Expected answer: 93

Correct? Yes

🔗 Problem

Problem: A quadrilateral shape has a perimeter of 255 m. The first and the second sides have lengths of 78m and 15m respectively, while the third side has a length of 63m. What is the length of the fourth side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides. So, the sum of the first three sides is 78m + 15m + 63m = 156m.
Therefore, the length of the fourth side is 255m - 156m = <<255-156=99>>99m.

### Answer: 99m 

Expected answer: 99

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides. 
The perimeter is the total length of all sides, so to find the length of one side, we divide the perimeter by 4: 128m / 4 = 32m.

### Answer: 32m 

Expected answer: 32

Correct? Yes

🔗 Problem

Problem: Imagine a rectangle with a perimeter of 96 feet. You know that one pair of opposite sides are each 33 feet long. Can you find the length of the other pair of opposite sides?

Gemini-1.5 Flash:

Here's how to solve this:

1. **Perimeter Formula:** The perimeter of a rectangle is calculated by adding up the lengths of all four sides.  The formula is: Perimeter = 2 * (length + width).

2. **We know:** 
   - Perimeter = 96 feet
   - One side (length) = 33 feet

3. **Substitute and Solve:**
   - 96 = 2 * (33 + width)
   - 96 = 66 + 2 * width
   - 96 - 66 = 2 * width
   - 30 = 2 * width
   - width = 30 / 2
   - width = 15 feet

**Therefore, the length of the other pair of opposite sides is 15 feet.** 
### Answer: 15 feet 

Expected answer: 15

Correct? Yes

🔗 Problem

Problem: The perimeter of a square field is 112 meters. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a square is the sum of the lengths of all its sides, and since all sides of a square are equal, we can find the length of one side by dividing the perimeter by 4. 

Therefore, the length of each side is 112 meters / 4 = 28 meters.

### Answer: 28 meters 

Expected answer: 28

Correct? Yes

🔗 Problem

Problem: The perimeter of a square is 32 cm. Can you find the length of one of its sides?

Gemini-1.5 Flash:

Here's how to find the length of one side of the square:

* **Perimeter of a square:** The perimeter is the total length of all its sides. 
* **Square properties:** All sides of a square are equal in length.

Since the perimeter is 32 cm, and a square has 4 sides, each side is 32 cm / 4 = 8 cm.

### Answer: 8 cm 

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 364m. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning: A square has four equal sides. The perimeter is the total length of all the sides.  Therefore, to find the length of one side, we divide the perimeter by 4.

364 meters / 4 = 91 meters. 

### Answer: 91 meters 

Expected answer: 91

Correct? Yes

🔗 Problem

Problem: The total perimeter of a rectangle is found to be 144 feet. The length of one side is known to be 38 feet. What is the length of the other side of the rectangle in feet?

Gemini-1.5 Flash:

Reasoning: A rectangle has two pairs of equal sides. We know one side is 38 feet long, so the opposite side is also 38 feet long.  The total length of these two sides is 38 + 38 = 76 feet.
The total perimeter of the rectangle is 144 feet, and 76 feet of that is accounted for by the two known sides.  That means the remaining two sides must have a total length of 144 - 76 = 68 feet.
Since both of those sides are equal, each side must be 68/2 = 34 feet long.

### Answer: 34 

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 205m. Two of its sides add up to 54m and the other two sides add up to 22m and 37m respectively. What is the length of the remaining side to complete the perimeter?

Gemini-1.5 Flash:

Reasoning: We know the perimeter is 205m.  The two sides that add up to 22m and 37m are 59m in total.  The two sides that add up to 54m along with the 59m total a combined length of 113m.  Since the perimeter is 205m, the remaining side must be 205m - 113m = 92m.

### Answer: 92m

Expected answer: 92

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: The perimeter of a rectangle is calculated by adding up the lengths of all its sides.  We know the length is 65m, and the perimeter is 174m. Since a rectangle has two lengths and two widths, we can set up the equation: 
2 * (length) + 2 * (width) = perimeter

Let's plug in the values we know:
2 * (65m) + 2 * (width) = 174m
130m + 2 * (width) = 174m

Now let's solve for the width:
2 * (width) = 174m - 130m
2 * (width) = 44m
width = 44m / 2 
width = 22m

### Answer: 22m 

Expected answer: 22

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides.  We know the lengths of three sides: 25 cm, 17 cm, and 89 cm.  Their sum is 25 + 17 + 89 = 131 cm.  Since the perimeter is 176 cm, the fourth side must have length 176 - 131 = 45 cm. 

### Answer: 45 cm 

Expected answer: 45

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 372 meters. What is the length of each side?

Gemini-1.5 Flash:

Reasoning:  A square has four equal sides.  To find the length of one side, we divide the perimeter by 4. 
 
 The length of each side is 372 meters / 4 = 93 meters.

### Answer: 93 meters 

Expected answer: 93

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Here's how to find the length of one side:

* **Perimeter of a square:** The perimeter is the total distance around the square.  It's calculated by adding up the lengths of all four sides.
* **Formula:**  Perimeter = 4 * side 
* **Solving for the side:**  We know the perimeter is 240 meters. So, 240 = 4 * side
* **Divide both sides by 4:**  240 / 4 = side
* **Calculate:** 60 = side

### Answer: 60 meters 

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: The perimeter of a rectangle is 242 meters. Knowing that one of the sides of this rectangle is 97 meters, can you determine the length of the other side?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Perimeter Formula:** The perimeter of a rectangle is calculated by adding up the lengths of all its sides: Perimeter = 2 * (length + width).

2. **Given Information:** We know the perimeter (242 meters) and one side (97 meters).  Let's assume the known side is the length.

3. **Substitute and Solve:**
   * 242 = 2 * (97 + width)
   * 242 = 194 + 2 * width
   * 242 - 194 = 2 * width
   * 48 = 2 * width
   * width = 48 / 2 
   * width = 24 meters

### Answer: 24 meters 

Expected answer: 24

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Here's how to solve this:

* **Understanding Perimeter:** The perimeter of a square is the total length of all its sides added together. Since a square has 4 equal sides, we can find the length of one side by dividing the perimeter by 4.

* **Calculation:**  316 meters (perimeter) / 4 sides = 79 meters per side.

### Answer: 79 

Expected answer: 79

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 268cm. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning: The perimeter of a square is the total length of all its sides. Since a square has 4 equal sides, we can find the length of one side by dividing the perimeter by 4. 
 
 So, the length of one side is 268cm / 4 = 67cm.

### Answer: 67cm 

Expected answer: 67

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 348m. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning:  A square has four equal sides.  To find the length of one side, we divide the perimeter by 4: 348m / 4 = 87m.

### Answer: 87m 

Expected answer: 87

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 400m. What is the length of one of its sides?

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  Therefore, the length of one side is equal to the perimeter divided by 4. 
The length of one side of the square is 400m/4 = 100m.
### Answer: 100m 

Expected answer: 100

Correct? Yes

🔗 Problem

Problem: A quadrilateral has sides with lengths of 81m, 100m, and 19m. If its perimeter is 243m, what is the length of the fourth side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its four sides. So, the length of the fourth side is equal to the perimeter minus the sum of the lengths of the other three sides. 
Therefore, the length of the fourth side is 243m - 81m - 100m - 19m = <<243-81-100-19=43>>43m.

### Answer: 43m 

Expected answer: 43

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 186cm. If one of its sides is 50cm long, how long is the other side?

Gemini-1.5 Flash:

Reasoning: We know that the perimeter of a rectangle is calculated by adding up the lengths of all its sides. Since a rectangle has two pairs of equal sides, we can represent the length of the unknown side as 'x'.  

Therefore, the perimeter can be represented as: 50cm + 50cm + x + x = 186cm.

Simplifying the equation: 100cm + 2x = 186cm

Subtracting 100cm from both sides: 2x = 86cm

Dividing both sides by 2: x = 43cm

### Answer: 43cm 

Expected answer: 43

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 224 cm. If the length of one of its sides is 78 cm, what is the length of the adjacent side?

Gemini-1.5 Flash:

Here's how to solve this problem:

1. **Perimeter and Rectangles:** The perimeter of a rectangle is the total length of all its sides.  Since a rectangle has two pairs of equal sides, we can represent the perimeter as: Perimeter = 2 * (length + width)

2. **Given Information:** We know the perimeter is 224 cm and one side (length) is 78 cm.

3. **Solve for the Width:**
   *  Let the unknown width be represented by "w".
   *  Plug in the known values: 224 = 2 * (78 + w)
   *  Simplify: 224 = 156 + 2w
   *  Subtract 156 from both sides: 68 = 2w
   *  Divide both sides by 2: w = 34 cm

### Answer: 34 cm 

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A quadrilateral has two sides measuring 79m and 97m. Another side measures 51m. The total perimeter of the quadrilateral is 235m. What is the length of the fourth side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides.
We know three sides measure 79m, 97m, and 51m, totaling 79+97+51=<<79+97+51=227>>227m.
The total perimeter is 235m, so the fourth side must be 235-227=<<235-227=8>>8 meters long.
### Answer: 8m

Expected answer: 8

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Here's how to calculate the length of one side of the square:

* **Understanding Perimeter:** The perimeter of a square is the total length of all its sides added together.
* **Formula:** Since a square has 4 equal sides, the perimeter is calculated as: Perimeter = 4 * side length
* **Solving for Side Length:**  We know the perimeter is 28m. Let 's' represent the side length. We can set up the equation: 28 = 4 * s
* **Isolate the side length:**  Divide both sides of the equation by 4: 28 / 4 = s
* **Calculate:** 7 = s

### Answer: 7m 

Expected answer: 7

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has 4 equal sides. Therefore, the length of each side is the perimeter divided by 4.  48cm / 4 = 12cm. 

### Answer: 12cm 

Expected answer: 12

Correct? Yes

🔗 Problem

Problem: A square plot of land has a perimeter of 184 meters. Can you find the length of one side of the plot?

Gemini-1.5 Flash:

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

Calculation: 184 meters / 4 = 46 meters

### Answer: 46 meters 

Expected answer: 46

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 56 meters. What is the length of each side?

Gemini-1.5 Flash:

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

The length of each side is 56 meters / 4 = 14 meters.

### Answer: 14 meters 

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 157m. If one of its sides is 97m long, and the other two sides are 5m and 30m, respectively, what is the length of the fourth side to complete the perimeter?

Gemini-1.5 Flash:

Reasoning: The sum of the three known sides is 97m + 5m + 30m = 132m.
The length of the fourth side is the perimeter minus the sum of the three known sides, so 157m - 132m = 25m.

### Answer: 25m

Expected answer: 25

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of all its sides. So, we can find the length of the fourth side by subtracting the lengths of the first three sides from the total perimeter.

The sum of the lengths of the first three sides is 46m + 50m + 35m = 131m.

Therefore, the length of the fourth side is 173m - 131m = 42m.

### Answer: 42m 

Expected answer: 42

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning:  A square has four equal sides. The perimeter is the total length of all the sides added together. So, to find the length of one side, we divide the perimeter by 4.

72 cm / 4 = 18 cm

### Answer: 18 cm 

Expected answer: 18

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides. To find the length of one side, we divide the perimeter by 4.

352 m / 4 = 88 m

### Answer: 88 m 

Expected answer: 88

Correct? Yes

🔗 Problem

Problem: A rectangle has 23m for its length and has a total perimeter of 116m. What is the length of its width?

Gemini-1.5 Flash:

Here's how to solve the problem:

* **Perimeter Formula:** The perimeter of a rectangle is calculated by:  Perimeter = 2 * (length + width)
* **We know:**
    * Length = 23m
    * Perimeter = 116m
* **Let's plug in the values and solve for the width:**
    * 116 = 2 * (23 + width)
    * 116 = 46 + 2 * width
    * 116 - 46 = 2 * width
    * 70 = 2 * width
    * width = 70 / 2
    * width = 35m

### Answer: 35m 

Expected answer: 35

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

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 find the length of one side by dividing the perimeter by 4. 
So, the length of each side is 124m / 4 = 31m.

### Answer: 31m 

Expected answer: 31

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a total perimeter of 131m. Three of its sides have lengths 24m, 57m, and 17m respectively. What is the length of the fourth side?

Gemini-1.5 Flash:

Reasoning:  The total length of the three known sides is 24m + 57m + 17m = 98m.  The perimeter is the total length of all sides, so the fourth side must have a length of 131m - 98m = 33m. 

### Answer: 33m

Expected answer: 33

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 254m. One of its sides has a length of 89m. What is the length of the other side?

Gemini-1.5 Flash:

Here's how to solve this:

1. **Perimeter Formula:** The perimeter of a rectangle is calculated by adding up the lengths of all its sides: Perimeter = 2 * (length + width)
2. **Knowns:** We know the perimeter (254m) and one side (89m). Let's call the unknown side "width".
3. **Substitute:**  254 = 2 * (89 + width)
4. **Simplify:** 254 = 178 + 2 * width
5. **Isolate width:**  254 - 178 = 2 * width 
6. **Solve for width:** 76 = 2 * width
7. **Final Step:** width = 76 / 2 = 38m

### Answer: 38m 

Expected answer: 38

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: The perimeter of a square is the sum of the lengths of all its sides. Since a square has 4 equal sides, we can find the length of one side by dividing the perimeter by 4.  
 
Therefore, the length of each side is 208m / 4 = 52m.

### Answer: 52m 

Expected answer: 52

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 64m. What is the length of each side of the square?

Gemini-1.5 Flash:

Reasoning:  A square has 4 equal sides. The perimeter is the total length of all the sides. To find the length of one side, we divide the perimeter by 4. 

So, the length of each side is 64m / 4 = 16m.

### Answer: 16m 

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a total perimeter of 196 meters. The lengths of three of its sides combined is 183 meters (with one side being 92 meters and the other two sides being 29 and 62 meters respectively). Can you figure out the length of the fourth side?

Gemini-1.5 Flash:

Here's how to solve this problem:

1. **Combine the known lengths:** The three known sides add up to 92 + 29 + 62 = 183 meters.

2. **Subtract from the total perimeter:**  Since the total perimeter is 196 meters, the fourth side must be 196 - 183 = 13 meters long.

### Answer: 13 

Expected answer: 13

Correct? Yes

🔗 Problem

Problem: The perimeter of a quadrilateral is 191 units. If one side is 35 units in length, another side is 76 units, and the third side is 5 units, what is the length of the fourth side in units?

Gemini-1.5 Flash:

The perimeter of a quadrilateral is the sum of the lengths of all its sides.  We know three sides are 35, 76, and 5 units long, which adds up to 35+76+5 = <<35+76+5=116>>116 units.  Since the perimeter is 191 units, the length of the fourth side must be 191 - 116 = <<191-116=75>>75 units. 

### Answer: 75 

Expected answer: 75

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  So, to find the length of one side, we divide the perimeter by 4. 
 
 The length of each side is 104m / 4 = <<104/4=26>>26m.

### Answer: 26m 

Expected answer: 26

Correct? Yes

🔗 Problem

Problem: The perimeter of a rectangle is 198 cm. If the length of this rectangle is 90 cm, what is the width?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Understand Perimeter:** The perimeter of a rectangle is the total length of all its sides.  For a rectangle, it's calculated as: Perimeter = 2 * (length + width)

2. **Set up the Equation:** We know the perimeter (198 cm) and the length (90 cm). Let's represent the width with 'w': 
   198 = 2 * (90 + w)

3. **Solve for the Width:**
   * 198 = 180 + 2w
   * 198 - 180 = 2w
   * 18 = 2w
   * w = 18 / 2
   * w = 9

### Answer: 9 cm 

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: Jack is designing a rectangular garden with a total perimeter of 128 feet. He has already planned for one pair of opposite sides to be 47 feet each. What should be the length of the remaining two opposite sides?

Gemini-1.5 Flash:

Reasoning: The two sides that are 47 feet each add up to 47 * 2 = 94 feet of the total perimeter.
The remaining two opposite sides must add up to 128 - 94 = 34 feet.
Since these two sides are opposite and therefore equal, each side must be 34 / 2 = 17 feet long. 
### Answer: 17 

Expected answer: 17

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 356m. What is the length of one of its sides?

Gemini-1.5 Flash:

Reasoning: The perimeter of a square is the total length of all its sides, and all sides of a square are equal.  Therefore, to find the length of one side, we divide the perimeter by 4.

So, the length of one side of the square is 356m / 4 = <<356/4=89>>89m.

### Answer: 89m 

Expected answer: 89

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 236 units. Two sides of the quadrilateral measure 89 units and 87 units respectively, while the third side is 1 unit long. What is the length of the fourth side?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Perimeter:** The perimeter of a quadrilateral is the sum of the lengths of all its sides.
2. **Known Sides:** We know three sides: 89 units, 87 units, and 1 unit.
3. **Total Known Length:** The total length of the three known sides is 89 + 87 + 1 = 177 units.
4. **Fourth Side:** To find the length of the fourth side, subtract the total known length from the perimeter: 236 - 177 = 59 units.

### Answer: 59 

Expected answer: 59

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides. To find the length of one side, we divide the perimeter by 4. 
 
The length of one side is 340 meters / 4 = 85 meters.

### Answer: 85 meters 

Expected answer: 85

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has four equal sides.  The perimeter is the total length of all sides added together.  Therefore, to find the length of one side, we divide the perimeter by 4. 

16m / 4 = 4m

### Answer: 4m 

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A quadrilateral has four sides. The length of the first side is 1m, the second side is 54m, and the third side is 9m. The total perimeter of this quadrilateral is 81m. What would be the length of the fourth side in meters?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Understand perimeter:** The perimeter of a shape is the total length of all its sides.
2. **Add known sides:** The sum of the first three sides is 1m + 54m + 9m = 64m.
3. **Subtract from total perimeter:** To find the length of the fourth side, subtract the sum of the first three sides from the total perimeter: 81m - 64m = 17m.

### Answer: 17 

Expected answer: 17

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning:  A square has four equal sides.  Therefore, to find the length of one side, we divide the perimeter by 4.

The length of each side is 316m / 4 = 79m.

### Answer: 79m 

Expected answer: 79

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has 4 equal sides.  To find the length of one side, we can divide the perimeter by 4.  
300m / 4 = 75m

### Answer: 75m 

Expected answer: 75

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 198m. Two of the sides have lengths of 19m and 57m respectively, another side is 22m, what is the length of the remaining side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of the lengths of all its sides. We know that three sides are 19m, 57m, and 22m. The total length of these three sides is 19m + 57m + 22m = 98m.
The perimeter of the quadrilateral is 198m, so the remaining side must be 198m - 98m = 100m.
### Answer: 100m 

Expected answer: 100

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has 4 equal sides. The perimeter is the total length of all sides added together. Therefore, the length of one side is the perimeter divided by 4.

The length of one side is 172m / 4 = 43m. 

### Answer: 43m 

Expected answer: 43

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?

Gemini-1.5 Flash:

Reasoning: A square has 4 equal sides.  The perimeter of a square is the sum of all its sides, so to find the length of one side, we divide the perimeter by 4: 304 cm / 4 = 76 cm.

### Answer: 76 cm 

Expected answer: 76

Correct? Yes

🔗 Problem

Problem: A rectangle has a total perimeter of 158 meters. Each of the shorter sides is 51 meters long. What is the length of each of the longer sides?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Perimeter and Sides:** The perimeter of a rectangle is the total length of all its sides. We know the perimeter is 158 meters.

2. **Short Sides:** We know the length of each short side is 51 meters. Since there are two short sides, their total length is 51 meters * 2 = 102 meters.

3. **Longer Sides:**  Subtract the length of the short sides from the total perimeter to find the combined length of the longer sides: 158 meters - 102 meters = 56 meters.

4. **Individual Longer Side:** Divide the combined length of the longer sides by 2 to find the length of each individual longer side: 56 meters / 2 = 28 meters.

### Answer: 28 

Expected answer: 28

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has 4 equal sides. 
The perimeter of a square is found by adding the length of all its sides. 
Therefore, the length of one side of the square is 72m/4 = <<72/4=18>>18m. 

### Answer: 18m 

Expected answer: 18

Correct? Yes

🔗 Problem

Problem: A rectangular playground is bordered by a fence. Two opposite sides of the fence are 19m each. If the total length of the fence is 166m, what is the length of each of the other two sides?

Gemini-1.5 Flash:

Reasoning:  The two opposite sides of the rectangle that are 19 meters each account for 19 meters * 2 = 38 meters of the total fence length.  That means the remaining fence length is 166 meters - 38 meters = 128 meters. Since the opposite sides of a rectangle are equal, the other two sides each measure 128 meters / 2 = 64 meters.

### Answer: 64 

Expected answer: 64

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Here's how to solve this problem:

1. **Perimeter:** The perimeter of a quadrilateral is the sum of the lengths of all its sides.
2. **Known Sides:** We know three sides are 40m, 32m, and 95m.
3. **Finding the Fourth Side:** 
    * Add the lengths of the known sides: 40m + 32m + 95m = 167m
    * Subtract the sum of the known sides from the total perimeter: 246m - 167m = 79m

### Answer: 79m 

Expected answer: 79

Correct? Yes

🔗 Problem

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

Gemini-1.5 Flash:

Reasoning: A square has 4 equal sides. If the perimeter is 32m, each side must be 32m/4 = 8m long.

### Answer: 8m 

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 12 meters. Can you find the length of one side of the square?

Gemini-1.5 Flash:

Here's how to find the length of one side:

* **Perimeter of a square:** The perimeter is the total length of all its sides added together.
* **Square sides:** All sides of a square are equal in length.

Let's represent the length of one side of the square with the variable 's'.

* **Formula:** Perimeter = 4s (since there are 4 equal sides)

We know the perimeter is 12 meters:

* 12 = 4s

To find the length of one side ('s'), we need to solve for 's':

* 12 / 4 = s
* 3 = s

### Answer: 3 meters 

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 160m. If the three known sides have lengths of 29m, 16m, and 41m, what is the length of the fourth side?

Gemini-1.5 Flash:

Reasoning: The perimeter of a quadrilateral is the sum of the lengths of its four sides.  We know the lengths of three sides, so we can subtract their sum from the total perimeter to find the length of the fourth side. 

The sum of the three known sides is 29m + 16m + 41m = 86m.

Subtracting this sum from the total perimeter gives us 160m - 86m = 74m.

### Answer: 74m 

Expected answer: 74

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 98m. If one of its sides is 5m long, what is the length of the other side?

Gemini-1.5 Flash:

Here's how to solve the problem:

* **Perimeter Formula:** The perimeter of a rectangle is found by adding up the lengths of all its sides: Perimeter = 2 * (length + width).
* **We know:** 
    * Perimeter = 98m
    * One side (let's call it the width) = 5m
* **Let's find the length:**
    * 98 = 2 * (length + 5)
    * 98 = 2 * length + 10
    * 98 - 10 = 2 * length
    * 88 = 2 * length
    * length = 88 / 2
    * length = 44m

### Answer: 44m 

Expected answer: 44

Correct? Yes

🔗 Problem

Problem: A rectangle has two sides measuring 45m each. If the total perimeter of the rectangle is 210m, what is the length of each of the other two sides?

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Perimeter and Sides:** The perimeter of a rectangle is the total length of all its sides.  We know the perimeter is 210m.

2. **Known Sides:** We know two sides are 45m each, totaling 45m * 2 = 90m.

3. **Remaining Sides:**  Subtract the known sides from the total perimeter to find the length of the remaining two sides: 210m - 90m = 120m.

4. **Equal Sides:** Since the remaining sides are equal, each side is 120m / 2 = 60m.

### Answer: 60m 

Expected answer: 60

Correct? Yes