A square and rectangle both have an area of 16 square inches. If one of
the side of the rectangle is 2 inches, how many inches greater is the
perimeter of the rectangle?

Question

A square and rectangle both have an area of 16 square inches. If one of the side of the rectangle is 2 inches, how many inches greater is the perimeter of the rectangle?

UpStudy AI · Accepted Answer

To determine how many inches greater the perimeter of the rectangle is compared to the square, follow these steps:

1. **Calculate the side length of the square:**
   - The area of the square is $$16$$ square inches.
   - Since the area of a square is given by $$ \text{side}^2 $$, the side length is:
     $$
     \text{side} = \sqrt{16} = 4 \text{ inches}
     $$
   
2. **Determine the perimeter of the square:**
   - The perimeter $$P$$ of a square is $$4 \times \text{side}$$:
     $$
     P_{\text{square}} = 4 \times 4 = 16 \text{ inches}
     $$

3. **Find the dimensions of the rectangle:**
   - The area of the rectangle is also $$16$$ square inches.
   - Given that one side of the rectangle is $$2$$ inches, the other side can be calculated as:
     $$
     \text{other side} = \frac{\text{Area}}{\text{given side}} = \frac{16}{2} = 8 \text{ inches}
     $$

4. **Calculate the perimeter of the rectangle:**
   - The perimeter $$P$$ of a rectangle is $$2 \times (\text{length} + \text{width})$$:
     $$
     P_{\text{rectangle}} = 2 \times (2 + 8) = 2 \times 10 = 20 \text{ inches}
     $$

5. **Determine the difference in perimeters:**
   - Subtract the perimeter of the square from the perimeter of the rectangle:
     $$
     \text{Difference} = 20 - 16 = 4 \text{ inches}
     $$

**Answer:** 4
The rectangle's perimeter is 4 inches greater than the square's perimeter.

A square and rectangle both have an area of 16 square inches. If one of
the side of the rectangle is 2 inches, how many inches greater is the
perimeter of the rectangle?

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