If side of a square is doubled, then the new perimeter is____ times the original perimeter.

Options

A. 2
B. `(1)/(4)`
C. 9
D. 4

Answer

To solve the problem, we need to find out how the perimeter of a square changes when the side length is doubled.

### Step-by-Step Solution:

1. **Understand the formula for the perimeter of a square**:
The perimeter (P) of a square is calculated using the formula:
\[ P = 4 \times \text{side} \]

2. **Let the original side length of the square be 's'**:
So, the original perimeter (P₁) can be expressed as:
\[ P₁ = 4 \times s \]

3. **Double the side length**:
If the side length is doubled, the new side length becomes:
\[ \text{New side} = 2s \]

4. **Calculate the new perimeter (P₂)**:
Using the new side length, the new perimeter can be calculated as:
\[ P₂ = 4 \times (2s) = 8s \]

5. **Compare the new perimeter with the original perimeter**:
To find how many times the new perimeter is compared to the original perimeter, we can set up the ratio:
\[ \text{Ratio} = \frac{P₂}{P₁} = \frac{8s}{4s} \]

6. **Simplify the ratio**:
Simplifying the ratio gives:
\[ \text{Ratio} = \frac{8}{4} = 2 \]

### Conclusion:
Thus, if the side of a square is doubled, the new perimeter is **2 times** the original perimeter.