The percentage Increase in the area of a rectangle, if each of its sides is increased by 20%, is :

Options

A. 40%
B. 42%
C. 44%
D. 46%

Answer

To find the percentage increase in the area of a rectangle when each of its sides is increased by 20%, we can follow these steps:

### Step 1: Define the original dimensions
Let the original length of the rectangle be \( L \) and the original breadth be \( B \).

### Step 2: Calculate the new dimensions after the increase
If each side is increased by 20%, the new length \( L' \) and new breadth \( B' \) can be calculated as follows:
- New length \( L' = L + 20\% \text{ of } L = L + \frac{20}{100}L = L + \frac{1}{5}L = \frac{6}{5}L \)
- New breadth \( B' = B + 20\% \text{ of } B = B + \frac{20}{100}B = B + \frac{1}{5}B = \frac{6}{5}B \)

### Step 3: Calculate the original area
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

### Step 4: Calculate the new area
The new area \( A' \) of the rectangle after the increase in dimensions is:
\[ A' = L' \times B' = \left(\frac{6}{5}L\right) \times \left(\frac{6}{5}B\right) = \frac{36}{25}LB \]

### Step 5: Calculate the increase in area
The increase in area is given by:
\[ \text{Increase in Area} = A' - A = \frac{36}{25}LB - LB = \left(\frac{36}{25} - 1\right)LB = \left(\frac{36}{25} - \frac{25}{25}\right)LB = \frac{11}{25}LB \]

### Step 6: Calculate the percentage increase
The percentage increase in area is calculated as:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase in Area}}{\text{Original Area}}\right) \times 100 = \left(\frac{\frac{11}{25}LB}{LB}\right) \times 100 = \frac{11}{25} \times 100 \]
\[ = 44\% \]

### Conclusion
Thus, the percentage increase in the area of the rectangle when each of its sides is increased by 20% is **44%**.

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