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.


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