(Q.40) The area of a rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area will increase by 50 sq. units. Find the length and breadth of the rectangle.

Let the length of the rectangle = x units

breadth = y units Area = l . b = xy sq. units

By problem, (x – ) (y + ) = xy – and (x + ) (y – ) = xy +

⇒ xy + x – y – 10 = xy – and xy – x + y – 50 = xy +

⇒ x – y = xy – – xy + 10 and -x + y = xy + – xy +

⇒ x – y = – and -x + y =

2x - 5y = -70
x y (x,y)
10 (10,)
20 (20,)
-5x + 10y = 100
x y (x,y)
0 (0,)
-10 (-10,)

The two lines intersect at the point (, )

∴ The solution is x = and y =

i.e., length = units; breadth = units.