Question

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?

Answer 1

length`=80cm`

Explanation:

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