Problem
2012 AMC 8 Problem 25
A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each 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?
![[asy] draw((0,2)--(2,2)--(2,0)--(0,0)--cycle); draw((0,0.3)--(0.3,2)--(2,1.7)--(1.7,0)--cycle); label("$a$",(-0.1,0.15)); label("$b$",(-0.1,1.15));[/asy]](/static/aops/3d4cdd3dbcabe3dc76b806d60b785416afc65f11.png)
\textbf{(A)}\ \frac{1}5\qquad\textbf{(B)}\ \frac{2}5\qquad\textbf{(C)}\ \frac{1}2\qquad\textbf{(D)}\ 1\qquad\textbf{(E)}\ 4
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