Four congruent rectangles are placed as shown. The area of the outer square is $9$ 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?

1. Assume the longer side is $a$ and the shorter side is $b$. Then $(a+b)^2= 9 (a-b)^2$, $a+b=3(a-b)$, $a=2b$.
2. The ratio is $2$.