Question

The area of a rectangle gets reduced by 67 square meters, when its length is increased by 3m and the breadth is decreased by 4m. If the length is reduced by 1m and breadth is increased by 4m, the area is increased by 89 square meters, Find the dimension of the rectangle.

Answer 1

Let the length and the breadth of the rectangle be x m and y m, respectively.
Case 1: When length is increased by 3m and the breadth is decreased by 4m:
xy – (x + 3) (y – 4) = 67
⇒ xy – xy + 4x – 3y + 12 = 67
⇒ 4x – 3y = 55                     ………(i)
Case 2: When length is reduced by 1m and breadth is increased by 4m:
(x – 1) (y + 4) – xy = 89
⇒ xy + 4x – y – 4 – xy = 89
⇒ 4x – y = 93                     ………(ii)
Subtracting (i) and (ii), we get:
2y = 38⇒ y = 19
On substituting y = 19 in (ii), we have
4x – 19 = 93
⇒4x = 93 + 19 = 112
⇒x = 28
Hence, the length = 28m and breadth = 19m.