Question

if the length and the breadth of a rectangle is increased by a% and b% respectively then the area will increase by​

Answer 1

The percentage increase in area will be $[(1 + \frac{a}{100})( 1 + \frac{b}{100}) - 1] \times 100 \%$.

Step-by-step explanation:

Let the length of the rectangle originally is L and breadth is B.

So, the original area of the rectangle will be, A = LB ......... (1)

If the length is increased by a%, then the length will become  $L(1 + \frac{a}{100})$ and if the breadth is increased by b%, then the breadth will become $B(1 + \frac{b}{100})$ .

Therefore, the area finally will become $A' = LB(1 + \frac{a}{100})(1 + \frac{b}{100})$

Therefore, the percentage increase in the area will be

$\frac{A' - A}{A} \times 100$

= $[(1 + \frac{a}{100})( 1 + \frac{b}{100}) - 1] \times 100 \%$ (Answer)