Answer
$A(x)=10x-x^2$, $0\lt x \lt10$
Work Step by Step
We are told that the rectangle has perimeter of 20 ft ($p=20$). We know that:
$A=l*w$
$P=2l+2w=20$
We solve for $l$:
$2l+2w=20$
$2l=20-2w$
$l=10-w$
We substitute:
$A=l*w=(10-w)w=10w-w^2$
If we use $x$ for $w$, then:
$A(x)=10x-x^2$
(And $0\lt x \lt10$ to keep length and width positive.)
