Question

The perimeter of a rectangular field is 80 m. If the breadth is increased by 2 m and the length is decreased by 2 m, the area of the field increases by 36 m². Find the length and the breadth of the field.

Answer 1

Let the breadth of the rectangle be x cm.
Perimeter of the rectangle = 80
⇒ 2(l + x) = 80
⇒ l + x = 40
⇒ l = 40 - x
So, the area = lb = x(40 - x) = 40x - x²
breadth = (x + 2)m
length = (40 - x - 2)m = (38 - x)m
So, area
= (38 - x)(x + 2) 
= 38x + 76 - x² - 2x
= x² + 36x + 76
As per the given condition,
-x² + 36x + 76 - (40x - x²)
⇒ -x² + 36x + 76 - 40x + x² = 36
⇒ 36x + 76 - 40x = 36
⇒ -4x = -40
⇒ x = 10
So, breadth = 10m and  length = 40 -x = 30m
Hence, the breadth is 10m and the  length is 30m.