if in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 sq. 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.

Let L and B units be the length and breadth of the rectangle.

When the length is increased by 2 units, then the length will be = L+2

and breadth reduced  by 2 units, then breadth will be = B-2

∴Acc. to the question,

Now, 

when the length is reduced by 1 unit , then the length will be = L-1

and 

the breadth increased by 2 units, the breadth will be = B+2

Now, On subtracting (i) and (ii), we get,

⇒L-B-2L + B = 12-35

⇒-L  = -23

L= 23 units.

Put the value of L in equation (i), we get,

⇒L-B=12

⇒23-B=12

B = 11 units.

Area of rectangle = L B = 2311 = 253 sq. units.

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