The length of a rectangli is decreased by 20 percentage then the percentage of width be increased to maintain the same area is?
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2
area of rectangle= lb
if length is decreased by 20%
l' = l - 0.2l = 0.8l
let width = b'
area is same
l'b' = lb
(0.8l) × b' = lb
b' = lb/0.8l
b' = b/0.8 = 1.25b
increase in b = 1.25b - b = 0.25b
% increased = 0.25b/b × 100 = 25%
Width should be increased by 25%
if length is decreased by 20%
l' = l - 0.2l = 0.8l
let width = b'
area is same
l'b' = lb
(0.8l) × b' = lb
b' = lb/0.8l
b' = b/0.8 = 1.25b
increase in b = 1.25b - b = 0.25b
% increased = 0.25b/b × 100 = 25%
Width should be increased by 25%
Answered by
0
Let the original length be l
New length =l− 20/100 l=0.8l
Original width =b
New width =b+x
Original Area=New Area
lb=(0.8l)(b+x)
⇒lb=0.8lb+0.8lb
⇒0.2lb=0.8lx
⇒x= b/4
%increase= x/b ×100
= b/4×b×100=25%
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