Question

In a rectangle, the length is increased and breadth is reduced by 2 units each, the area is reduced by 28 square units .If the length is reduced by 1 unit, and the breadth increased by 2 units , the area is increased by 33 units . find the dimensions of the rectangle.

Answer 1

let the length and breadth of rectangle be
x and y units.
area of rectangle = xy square units
$(x + 2)(y - 2) = xy - 28 \\ (x - 1)(y + 2) = xy + 33$

from statement we can write these two equations,now solve for value of x and y
$xy - 2x + 2y - 4 = xy - 28 \\ - 2x + 2y = - 24 \\ xy + 2x - y - 2 = xy + 33 \\ 2x - y = 35$
add both equations to eliminate x
$y = - 24 + 35 = 11 \\ 2x - 11 = 35 \\ 2x = 46 = x = 23$
so length is 23 units and breadth is 11 units.
area of rectangle= 23x11=253 square units