Question

The perimeter of a rectangular field is 100m. If its length is decreased by 2m and breadth increased by 3 m, the area of the field is increased by 44m². Find the dimensions 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) = 100m
⇒ x + y = 50m ----(1)
Original area = xy m²
New increased length = (x - 2)m
New deacreased breadth = (y + 3)m
Then, new area = (x - 2)(y + 3)m²
Also, its length is decreased by 2m and breadth increased by 3m, the area of the field us uncreased by 44m²
⇒ (x - 2)(y + 3)m² = (xy + 44)m²
⇒ (xy - 2y + 3x - 6)m² = (xy + 44)m²
⇒ 3x - 2y = 50 ----(2)
Solving (1) and (2), we get:
y = 20m and x = 30m.
Thus, the length of the rectangular field is 30m and breadth is 20m.