Question

The area of a rectangle gets reduced by 8m²,if its length is reduced by 5m and breadth increased by 3m. If we increase the length by 3m and breadth by 2m, the area is increased by 74m². Find the length and breadth of the rectangle.

Answer 1

let x=length of rectangle
let y=breadth of rectangle
original area=xy
xy-(x-5)(y+3)=8
(x+3)(y+2)-xy=74
..
xy-(xy-5y+3x-15)=8
-xy+(xy+3y+2x+6)=74
..
xy-xy+5y-3x+15=8
-xy+xy+3y+2x+6=74
..
5y-3x+15=8
3y+2x+6=74
..
10y-6x+30=16
9y+6x+18=222
add
19y+48=238
19y=190
y=10
2x=74-6-3y=38
x=19
length of rectangle=19 metres
breadth of rectangle=10 meters