AMC 8 2012 Problem 25

A square with area $4$ is inscribed in a square with area $5$, with each vertex of the smaller square on a side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length $a$, and the other of length $b$. What is the value of $ab$?

$\textbf{(A)}\hspace{.05in}\frac{1}5 \textbf{(B)}\hspace{.05in}\frac{2}5 \textbf{(C)}\hspace{.05in}\frac{1}2 \textbf{(D)}\hspace{.05in}1 \textbf{(E)}\hspace{.05in}4$