A circle of radius 5 is inscribed in a rectangle as shown.  The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?
[asy] draw((0,0)--(0,10)--(20,10)--(20,0)--cycle);  draw(circle((10,5),5));[/asy]
$\textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\  125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200$
Note that the diameter of the circle is equal to the shorter side of the rectangle. Since the radius is $5$, the diameter is $2\cdot 5 = 10$.
Since the sides of the rectangle are in a $2:1$ ratio, the longer side has length $2\cdot 10 = 20$.
Therefore the area is $20\cdot 10 = 200$ or $\boxed{\textbf{(E)}\ 200}$