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,
when the length is reduced by 1 unit , then the length will be = L-1
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,
⇒B = 11 units.
Area of rectangle = L B = 2311 = 253 sq. units.