If the side of a square is Increased by 20%, then what will be the percentage increase in its perimeter?

Options

A. 20
B. 40
C. 100
D. 50

Answer

To solve the problem of finding the percentage increase in the perimeter of a square when its side is increased by 20%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the side and perimeter of a square**:
- The perimeter (P) of a square is given by the formula:
\[ P = 4 \times \text{side} \]

2. **Let the original side length of the square be \( s \)**.

3. **Calculate the new side length after a 20% increase**:
- A 20% increase means the new side length (s') can be calculated as:
\[ s' = s + 0.20s = 1.20s \]

4. **Calculate the original perimeter**:
- Using the original side length:
\[ P_{\text{original}} = 4s \]

5. **Calculate the new perimeter with the increased side length**:
- Using the new side length:
\[ P_{\text{new}} = 4s' = 4(1.20s) = 4.8s \]

6. **Determine the change in perimeter**:
- The change in perimeter (ΔP) is:
\[ \Delta P = P_{\text{new}} - P_{\text{original}} = 4.8s - 4s = 0.8s \]

7. **Calculate the percentage increase in perimeter**:
- The percentage increase can be calculated using the formula:
\[ \text{Percentage Increase} = \left(\frac{\Delta P}{P_{\text{original}}}\right) \times 100 \]
- Substituting the values:
\[ \text{Percentage Increase} = \left(\frac{0.8s}{4s}\right) \times 100 = \left(\frac{0.8}{4}\right) \times 100 = 20\% \]

### Final Answer:
The percentage increase in the perimeter of the square is **20%**.