Question

If the length of a rectangle is increased by 20% and breadth is decreased by 20%, then what will be percentage decrease in area?

Answer 1

Let initial dimensions be l and b.

Area = l*b

new length = 1.2 l

new breadth = 0.8 b

New Area = 1.2 l * 0.8 b

percent decrease = ((Original Area - New area) * 100%) / Original area

= 4%

Answer 2

let the initial length and breadth of rectangle be l $b

length is increased by 20%
then new length=l+l×20/100
=l + 0.2l=1.2l
breadth is decreased by 20%
then new length =b-b×20/100
=b-0.2b=0.8b

area = 1.2b×0.8b=0.96b

decrease in area =lb-0.96lb=0.04lb

percentage decrease=0.04lb/lb ×100%=4%



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