If the length of a rectangle is reduced by 5 units and its breadth is increased by 2 units then the area of the rectangle is reduced by 80 sq units. However, if we increase its length by 10 units and decrease the breadth by 5 units, its area increased by 50 sq units. Find the length and breadth of the rectangle.

Explanation

Let the length and breadth of the rectangle be x units and y units respectively.
Then, area of the rectangle = xy sq units.
Case I When the length is reduced by 5 units and the breadth is increased by 2 units.
Then, new length = `( x - 5)` units.
and new breadth ` = ( y +2 )` units.
` therefore ` new area = ` (x - 5) ( y + 2 )` sq units.
` therefore xy - (x - 5 ) ( y +2 ) = 80 rArr 5y - 2 x = 70" " `... (i)
Case II When the length is increased by 10 units and the breadth is decreased by 5 units.
Then, new length = ` ( x + 10 ) ` units.
and new breadth `= ( y - 5) ` units.
` therefore ` new area = ` (x + 10) ( y - 5) `sq units.
` therefore (x+ 10 ) ( y - 5) - xy = 50 `
`rArr 10 y - 5 x = 100 rArr 2y - x = 20 " " `... (ii)
On multiplying (ii) by 2 and subtracting the result from (i), we get ` y = 30 `.
Putting ` y = 30 ` in (ii), we get
` ( 2 xx 30 ) - x = 20 rArr 60 - x = 20 rArr x = ( 60 - 20 ) = 40 `
` therefore x = 40 and y = 30 `
Hence, length = 40 units and breadth = 30 units.