Question

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm² more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answer 1

Let the breadth of the rectangle be x meter

Length of the rectangle be (x + 9) meter

Area of the rectangle length×breadth = x(x +9) m²

When length and breadth increased by 3cm then,

New length = x + 9 + 3 = x + 12

New breadth = x + 3

So, Area is

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

x² + 15x + 36 = x² + 9x + 84

15x – 9x = 84 – 36

6x = 48

x = 48/6

= 8

∴ Length of the rectangle (x + 9) = (8 + 9) = 17cm and breadth of the rectangle is 8cm.