Question

The length of the rectangle is greater than its breadth by 2 cm. The area of the rectangle is 24 sq.cm, find its length and breadth.

Answer 1

Let the breadth of the rectangle be x cm. Then, the length of the rectangle will be (x + 2) cm.
Thus, by the given condition, we have
(x + 2) × x = 24
$\Rightarrow$ x² + 2x = 24
$\Rightarrow$ x² + 2x – 24 = 0
On splitting the middle term 2x as 6x – 4x, we get:
x² + 6x – 4x – 24 = 0
$\Rightarrow$ x(x + 6) – 4(x + 6) = 0
$\Rightarrow$ (x + 6)(x – 4) = 0
$\Rightarrow$ x + 6 = 0 or x – 4 = 0
$\Rightarrow$ x = –6 or x = 4
Since the breadth of the rectangle cannot be negative, x = 4.
Thus, the breadth of the rectangle is 4 cm and the length of the rectangle is (x + 2=) 6 cm.