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

let the breadth be x

length: x+9 , breadth: x

length and breadth are incresed by 3 so,

length: x+9 +3 = x+12 ,breadth: x+3

Gn: the area of the new rectangle = 84 sq. cm

Equation:

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

x² + 15x + 36 = 84 + x² +9x

if we transpose x²to the opposite side then it becomes x²

x² x² + 15x + 36 = 84 + 9x

Now it becomes 15x+36 = 84 +9x

If we transpose 9x to the opposite side it becomes 15x +36 9x = 84

6x +36 = 84

6x = 84 36

6x= 48

x=48/6

x=8

length : 8+9 = 17

breadth= 8