The-length-of-a-rectangle-is-decreased-by-20-and-the-width-is-increased-by-x-but-the-area-remains-the-same-Find-the-value-of-x-

Question Number 119386 by ZiYangLee last updated on 24/Oct/20

The length of a rectangle is decreased by 20 %,

and the width is increased by x %,

but the area remains the same .

Find the value of x .

Answered by mr W last updated on 24/Oct/20

(1 - \frac{20}{100}) L \times (1 + \frac{x}{100}) W = L \times W

(1 - \frac{20}{100}) (1 + \frac{x}{100}) = 1

1 + \frac{x}{100} = \frac{100}{80}

x = \frac{100}{4} = 25

Commented by ZiYangLee last updated on 24/Oct/20

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Answered by som(math1967) last updated on 24/Oct/20

l e t l e n g t h = l u n i t

w i d t h = b u n i t

∴ \frac{80 l}{100} \times \frac{(100 + x) b}{100} = l \times b

\Rightarrow (100 + x) = \frac{100 \times 100}{80}

∴ x = 125 - 100 = 25 a n s

Commented by ZiYangLee last updated on 24/Oct/20

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