Question

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are eachincreased by 3 cm, the area of the new rectangle will be $84c{m}^2$ more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answer 1

Let breadth of the rectangle = x cm Then length =(x + 9)cm

$\therefore$ Area = length $\times$ breadth $=x(x+9)c{m}^2$ By increasing each length and breadth by 3 cm

The new length of the rectangle = x + 9 + 3 = (x + 12) cm and breadth = (x + 3) cm

$\therefore$ Area = (x + 12)(x + 3)

According to the condition :

(x + 12)(x + 3) - x(x + 9) = 84

$\Rightarrow 6x=84-36=48\Rightarrow x=\frac{48}{6}=8$

$\therefore$ Length of the rectangle = x + 9 = 8 + 9 = 17 cm and breadth = x = 8 cm.