Answer
length of 25 and width of 25
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.
$w+h=50$
$w+h-h=50-h$
$w=50-h$
$h*(50-h)$
$50h-h^2=y$
$y=-h^2+50h$
$a=-1$, $b=50$, $c=0$
$x=-b/2a$
$x=-50/2*-1$
$x=-50/-2$
$x=25$
$h*(50-h)$
$25*(50-25)$
$25*25$
$625$
25 and 25 are the dimensions
