### Question Detail

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

- 32%
- 34%
- 42%
- 44%

**Answer: ** Option **D**

**Explanation:**

Let original length = x metres and original breadth = y metres.

\begin{aligned}

\text{Original area } = \text{xy } m^2 \\

\text{New Length }= \frac{120}{100}x = \frac{6}{5}x \\

\text{New Breadth }= \frac{120}{100}y = \frac{6}{5}y \\

=>\text{New Area }= \frac{6}{5}x * \frac{6}{5}y \\

=>\text{New Area }= \frac{36}{25}xy \\

\text{Area Difference} = \frac{36}{25}xy - xy \\

= \frac{11}{25}xy \\

Increase \% = \frac{Differnce}{Actual}*100 \\

= \frac{11xy}{25}*\frac{1}{xy}*100 = 44\%

\end{aligned}