2007 Cayley Problem 25

In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points W, X, Y, and Z is a vertex of one of the small squares. Square ABCD can be constructed with sides passing through W, X, Y, and Z. The maximum possible distance from A to P is closest to

\textbf{(A)}\ 5.2\quad \textbf{(B)}\ 5.4\quad \textbf{(C)}\ 5.6\quad \textbf{(D)}\ 5.8\quad \textbf{(E)}\ 6.0

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.