# 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.

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