Area of a rectangle = l × b

Given, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres.

⇒ (l + 3)(b – 4) = lb – 67

⇒ 3b – 4l = -55 ------ (1)

Also, (l – 1)(b + 4) = lb + 89

⇒ 4l – b = 93 ------- (2)

Adding (1) and (2), we get

⇒2 b = 38

⇒ b = 19

Thus, 4l – 19 = 93

⇒ l = 28m