Question

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

Answer 1

Let the length of the rectangular field be x m and breadth be y m.
Given, the perimeter of a rectangular field is 80m.
⇒ 2(x + y) = 80m
⇒ x + y = 40m -----(1)
Original area = xym² 
New increased length = (x + 2)m
New decreased breadth = (y - 2)m
Then, new area = (x + 2) (y - 2)m² 
Also, given the breadth is increased by 2m and the length is decreased by 2m, the area of the field in creases by 36m² 
⇒ (x + 2)(y - 2)m² = (xy + 36)m²
⇒ (Xy + 2y - 2x - 4)m² = (xy + 36)m²
⇒ 2(y - x) = 40m²
⇒ (y -x) = 20 ----(2)
Solving (1) and (2), we get:
y = 30m and x = 10m.
Thus, the length of the rectangular field is 10m and breadth is 30m.