AMC 12 2009a Problem 8

Four congruent rectangles are placed as shown. The area of the outer square is $4$ times that of the inner square. What is the ratio of the length of the longer side of each rectangle to the length of its shorter side?

unitsize(6mm);
defaultpen(linewidth(.8pt));

path p=(1,1)--(-2,1)--(-2,2)--(1,2);
draw(p);
draw(rotate(90)*p);
draw(rotate(180)*p);
draw(rotate(270)*p);

\textbf{(A)}\ 3 \textbf{(B)}\ \sqrt {10} \textbf{(C)}\ 2 + \sqrt2 \textbf{(D)}\ 2\sqrt3 \textbf{(E)}\ 4