Answer
$P(x)=\frac{32}{x}+2x$, $x>0$
Work Step by Step
We know that the area of the rectangle is:
$A=lw=16$
We can solve this for $l$:
$l=\frac{16}{w}$
We plug this into the perimeter formula:
$P=2l+2w=2(\frac{16}{w})+2w=\frac{32}{w}+2w$
(With $w>0$.)
If we use $x$ for $w$, then:
$P(x)=\frac{32}{x}+2x$, $x>0$
