If the length and the breadth of a rectangle are each increased by 1 metre, the area of the rectangle is increased by 22 square metres. If the length is decreased by 2 metres and the breadth is increased by 3 metres, the area is increased by 12 square metres. Find the perimeter of the rectangle.
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the length and the breadth of a rectangle are each increased by 1 metre, the area of the rectangle is increased by 22 square metres. If the length is decreased by 2 metres and the breadth is increased by 3 metres, the area is increased by 12 square metres. Find the perimeter of the rectangle.
Step-by-step explanation:
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Step-by-step explanation:
let the length and breadth of room be l and b respectively
area of room=lb
after increasing length by 1m=(l+1)
after increasing breadth by 1m=(b+1)
now, according to the question,
(l+1)(b+1)=lb+21
(l+1)(b+1)−lb=21
l+b=20⟶(1)
When, length increased by 1m and breadth is decreased by 1m, then
lb−[(l+1)(b−1)]=5
l−b=6⟶(2)
solving (1) & (2), we get
l=13 and b=7
∴ perimeter=2(l+b)m=2(13+7)=40m
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