The width of a rectangular box is 20% of the length. If the perimeter is 192 cm, then what are the length and width of the box?

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Answer 1 · 2017-07-06T19:00:12

length $=80cm$

Let the width be $w$
Let the length be $L$
Let perimeter be $p$

Drop the units of measurement for now

Then $p=2w+2L = 2(w+L)$

but $w=20/100L$ so by substitution we have:

$p=192=2(20/100L+L)$

Factor out $L$

$192=2L(20/100+1)$

but $20/100+1$ is the same as $20/100+100/100=120/100$

$192=cancel(2)^1L(120/(cancel(100)^50))$

$L=192xx50/120=80$

$L=80cm$
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check

width = $20/100L = 20/100xx80=16$

$2w+2L->2(80)+2(16)=192$ as required