If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.
Area of a rectangle = l × b
Given, if in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units.
⇒ (l + 2)(b – 2) = lb – 28
⇒ 2b – 2l = - 24 ------ (1)
Also, (l – 1)(b + 2) = lb + 33
⇒ 2l – b = 35 ------- (2)
Adding (1) and (2), we get
⇒ b = 11
Thus, 2l = 46, l = 23
Area of the rectangle = lb = 253 square units.