If each side of a rectangle is increased by 25%, then its area will increase by:

Correct option is B

Given:
Each side of a rectangle is increased by 25%. We need to find the percentage increase in its area.
Solution:
Let the original length and width of the rectangle be L and W respectively.
Original area, $$A_{\text{original}} = L \times W$$​​
After increasing each side by 25%, the new length and width become 1.25L and 1.25W respectively.
New area, $$A_{\text{new}} = 1.25L \times 1.25W = 1.5625 \times L \times W .$$​
The increase in area is $$A_{\text{new}} - A_{\text{original}} = 1.5625LW - LW = 0.5625LW$$​
Percentage increase in area = $$\left( \frac{0.5625LW}{LW} \right) \times 100\% = 56.25\%$$=56$$\frac{1}{4}\%$$​​
Alternate Method 1:
When both dimensions of a rectangle are increased by x% the percentage increase in area can be calculated using the formula:
$$\text{Percentage Increase} = \left( \left(1 + \frac{x}{100}\right)^2 - 1 \right) \times 100\%$$​​
Here, x = 25 so:$$\text{Percentage Increase} = \left( \left(1 + \frac{25}{100}\right)^2 - 1 \right) \times 100\% = \left(1.25^2 - 1\right) \times 100\% = (1.5625 - 1) \times 100\% = 56.25\%$$=56$$\frac{1}{4}\%$$​​
​Alternate Method 2:

a + b +$$\frac{ab}{100}$$

So,

=25 + 25 +$$\frac{625}{100}$$

=50 + 6.25

=56.25%=$$56\frac{1}{4}\%$$