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

May 28, 2016

$f \left(w\right) = - w + 24$

Explanation:

Recall that the perimeter of a rectangle is given by,

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} P = 2 \left(l + w\right) \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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

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

$P = 2 \left(l + w\right)$

$48 = 2 \left(l + w\right)$

$\frac{48}{2} = l + w$

$l = 24 - w$

Replacing $l$ with $f \left(w\right)$,

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{f \left(w\right) = - w + 24} \textcolor{w h i t e}{\frac{a}{a}} |}}}$