Question

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If the length and breadth of a rectangular room are each increased by 1m, then the area of floor is increased by 21m² . If the length is increased by 1m and breadth is decreased by 1m , then the area is decreased by 7m². Find the perimeter of the floor.

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Answer 1

Answer:

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