If each side of a rectangle is increased by 50%, its area will increase by :

Answer: Option B

Let original length = $$l$$ metres and original breadth = b metres
Original area : $$=\left(lb\right)m^2$$
New length :
\begin{aligned} & = \left( {\frac{{150l}}{{100}}} \right)m \\ & = \left( {\frac{{3l}}{2}} \right)m \\ & \text{New breadth :} \\ & = \left( {\frac{{150b}}{{100}}} \right)m \\ & = \left( {\frac{{3b}}{2}} \right)m \\ & \text{New area :} \\ & = \left( {\frac{{3l}}{2} \times \frac{{3b}}{2}} \right){m^2} \\ & = \left( {\frac{{9lb}}{4}} \right){m^2} \\ & \text{Increase} = 1 - \frac{9lb}{4} = \frac{5lb}{4} \\ & \therefore \text{ Increase % :} \\ & = \left( {\frac{{5lb}}{4} \times \frac{1}{{lb}} \times 100} \right)\% \\ & = 125\% \\\end{aligned}