Answer
width of 20 and length of 20
Work Step by Step
The width and length are represented, respectively, with $w$ and $h$. We want the area to be as large as possible. This product is as large as possible as the vertex.
$w+h=40$
$w+h-h=40-h$
$w=40-h$
$h*(40-h)$
$40h-h^2=y$
$y=-h^2+40h$
$a=-1$, $b=40$, $c=0$
$x=-b/2a$
$x=-40/2*-1$
$x=-40/-2$
$x=20$
$h*(40-h)$
$20*(40-20)$
$20*20$
$400$
20 and 20 are the dimensions
