Question

The perimeter of a rectangular book is 48 inches. How do you express the length of the book as a function of the width?

Answer 1

`f(w)=-w+24`

Explanation:

Recall that the perimeter of a rectangle is given by,

`color(blue)(|bar(ul(color(white)(a/a)P=2(l+w)color(white)(a/a)|)))`

where:
`P=`perimeter
`l=`length
`w=`width

Hence, to create an expression for the length, substitute `48` for `P` and rearrange for `l`.

`P=2(l+w)`

`48=2(l+w)`

`48/2=l+w`

`l=24-w`

Replacing `l` with `f(w)`,

`color(green)(|bar(ul(color(white)(a/a)color(black)(f(w)=-w+24)color(white)(a/a)|)))`