Question

The perimeter of a rectangular field is 100 m. If its length is decreased by 2 m and breadth increased by 3 m, the area of the field is increased by 44 m². Find the dimensions of the field.

Answer 1

Let the breadth of the rectangle be x cm.
Perimeter of the rectangle = 100
⇒ 2(l + x) = 100
⇒ 1 + x = 50
⇒ l = 50 - x
So, the area = lb = x(50 - x) = 50x - x² 
breadth = (x + 3)m
length = (50 - x - 2)m = (48 - x)m
So, area
|= (48 - x)(x + 3)
= 48x + 144 - x² - 3x
= -x² + 45x + 144
As per the given condition,
-x² + 45x + 144 - (50x - x²) = 44
⇒ -x² + 45x + 144 - 50x + x² = 44
⇒ -5x = -100
⇒ x = 20
So, breadth = 20m and length = 50 - x = 30m
Hence, the breadth is 20m and the length is 30m.