Answer
$$\color{blue}{x=0.5\text{ft}}$$
Work Step by Step
$(\text{area of the outer rectangle})-(\text{area of the inner rectangle}=21)$
$12(10)-(12-2x)(10-2x)=21$
$120-(120-24x-20x+4x^2)=21$
$120-120+44x-4x^2=21$
$4x^2+44x=21$
$4x^2+44x-21=0$
Use the quadratic formula: $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\dfrac{-(44)\pm\sqrt{(44)^2-4(-4)(-21)}}{2(-4)}$
$x=\dfrac{-44\pm\sqrt{1600}}{-8}$
$x=\dfrac{-44+40}{-8}$ or $x=\dfrac{-44-40}{-8}$
$x=\dfrac{-4}{-8}$ or $x=\dfrac{-84}{-8}$
$x=0.5$ or $x=10.5$
Since 10.5ft is larger than the wall we know that:
$\color{blue}{x=0.5\text{ft}}$