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

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