Question

length of an rectangle is 6 cm is more than its width.if its length and breadth each is decreased by 3 cm,the area of new rectangle is decreased by 36 sq cm find the original length and breadth of the original rectangle[solve this question by linear method]

Answer 1

Let the length and the breadth of the rectangle be (x+6) and x respectively.

Area of the rectangle = product of length and breadth

or, x (x+6) = 112

or, x^2 + 6x - 112 = 0

Splitting the middle term here, we have :

x^2 + 14x - 8x - 112 = 0

or, x ( x + 14 ) - 8 ( x + 14 ) = 0

or, ( x + 14 ) (x - 8) = 0

or, x = 8 [ The value x = -14 is rejected since the breadth cannot be a negative quantity)

Thus, length = x + 6 = 14 cm