Question

If the length & breadth of a rectangular room are each increased by 1m, then the area of the floor is increased by 21 sq m. If the length is increased by 1m and breadth is decreased by 1m, then the area is decreased by 5 sq m. The perimeter of the floor is :

Answer 1

let l and b be the length and breadth of rectangular room .
Given,
length and breadth increased by 1m .
so that area increased by 21 sqm
so
(l+1)×(b+1) = (l×b)+21
or, lb+l+b+1=lb+21
or, l+b =20 ...... (i)
Also,
length is increased by 1m and breadth is decreased by 1m So that area decreased by 5sqm
so,
(l+1)×(b-1) =(l×b)-5
or, lb-l+b-1=lb-5
or, l-b= 4 ....(ii)
solving (i) and (ii)
l=12 and b=8
Also, the perimeter of rectangular room = 2 (l+b)
= 2 (12+8)
= 40m is right answer. hope it helps you . :)