Answer
$8\sqrt 5\approx17.89$ in and $4\sqrt 5\approx8.94$ in
Work Step by Step
Step 1. Assume the length of the rectangle is $x$ in and the width is $y$ in.
Step 2. As the diameter of the circle is 20in, use the Pythagorean's Theorem and the area condition, we get:
\begin{cases} x^2+y^2=20^2 \\ xy=160 \end{cases}
Step 3. The second equation gives $y=\frac{160}{x}$, use it in the first equation to get:
$x^2+(\frac{160}{x})^2=400$ or $x^4-400x^2+160^2=0$
Step 4. Factor the above equation as $(x^2-80)(x^2-320)=0$ which gives $x=4\sqrt 5, 8\sqrt 5$
Step 5. Since $x$ is the length, we have the answers as $x=8\sqrt 5\approx17.89$ in, $y=4\sqrt 5\approx8.94$ in
