Question

The area of a rectangle gets reduced by 8 sq. metre, if its length is reduced by 5 metre...​

Answer 1

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

***

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