Question

The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Find the length and breadth of the rectangle.

Answer 1

Let the length of the rectangle be x units and the breadth of the rectangle be y units.
`therefore` Area of rectangle = xy square units
According to given conditions.
(x - 5)(y + 3) = xy - 9
implies xy + 3x - 5y = xy - 9
implies 3x - 5y = 6 ...(1)
Also (x + 3)(y + 2) = xy + 67
implies xy + 2x + 3y + 6 = xy + 67
implies 2x + 3y = 61 ...(2)
Multiplying equation (1) by 3 and (2) by 5, we get
9x - 15y = 18 ...(3)
10x + 15y = 305 ...(4)
Adding equations (3) and (4), we get
19x = 323
implies x = 17
Substituting x = 17 in equation (1), we get
`3 xx 17 - 5y = 6`
implies 51 - 5y = 6
implies -5y = - 45
implies y = 9
Hence, the length of the rectangle is 17 units and breadth is 9 units.