Question

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.

Answer 1

Let breadth of the rectangle = x cm

then length = x + 7

Area = l $\times$ h = (x + 7) $\times$ x

In second case,

Length of the new rectangle = x + 7 - 4 = x + 3 cm

and breadth = x + 3

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

According to the condition,

$(x+3)(x+3)=x(x+7)x^2+3x+3x+9=x^2+7x\Rightarrow x^2+6x-7x-x^2=-9\Rightarrow -x=-9\Rightarrow x=9$

$\therefore$ Length of the original rectangle = x + 7 = 9 + 7 = 16 cm

and breadth = x = 9 cm.