Question

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

xy – (x + 3) (y – 4) = 67

⇒ xy – xy + 4x – 3y + 12 = 67

⇒ 4x – 3y = 55   ...(i)

Case 2:

When length is reduced by 1 m and breadth is increased by 4 m:

(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

⇒ 4x = 112

⇒ x = 28

Hence, the length = 28 m and breadth = 19 m.