Question

The perimeter of a rectangular field is 140 m. If the length of the field is increased by 2 m and the breadth decreased by 3m, the area is decreased by 66 m². 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 140m.
⇒ 2(x + y) = 140m
⇒ x + y = 70m ----(1)
Original area = xym²
New increased length = (x + 2)m
New decreased breadth = (y - 3)m
Then, new area = (x + 2)(y - 3)m²
Also, given the length of the field is incresased by 2m and the breadth decreased by 3m, the area is decreased by 66m²
⇒ (x + 2)(y - 3)m² = (xy - 66)m²
⇒ (xy + 2y - 3x - 6)m² = (xy - 66)m²
⇒ (2y - 2x) = -60
⇒ (2y - 3x) = -60----(2)
Solving (1) and (2), we get:
x = 40m and y = 30m.
Thus, the length of the rectangular field is 40m and breadth is 30m.