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

Answer: Option C

Let original length = x metres and original breadth = y metres
$$\begin{array}{rl}& \text{Original}\text{are}=\left(xy\right)m^2\\ & \text{New}\text{length}=\left(\frac{120}{100}x\right)m=\left(\frac{6}{5}x\right)m\\ & \text{New}\text{breadth}=\left(\frac{120}{100}y\right)m=\left(\frac{6}{5}y\right)m\\ & \text{New}\text{area}=\left(\frac{6}{5}x\times \frac{6}{5}y\right)m^2=\left(\frac{36}{25}xy\right)m^2\\ & \text{The}\text{difference}\text{between}\text{the}\text{original}\text{area = }xy\\ & \text{and}\text{new}\text{area}\frac{36}{25}xy\text{is}\\ & =\left(\frac{36}{25}\right)xy-xy\\ & =xy\left(\frac{36}{25}-1\right)\\ & =xy\left(\frac{11}{25}\right)or\left(\frac{11}{25}\right)xy\\ & \therefore \text{Increase}\%\\ & =\left(\frac{11}{25}xy\times \frac{1}{xy}\times 100\right)\%\\ & =44\%\end{array}$$