2007 AMC 10B Problem 21

Right \triangle ABC has AB=3, BC=4, and AC=5. Square XYZW is inscribed in \triangle ABC with X and Y on \overline{AC}, W on \overline{AB}, and Z on \overline{BC}. What is the side length of the square?

\textbf{(A) } \frac{3}{2} \qquad\textbf{(B) } \frac{60}{37} \qquad\textbf{(C) } \frac{12}{7} \qquad\textbf{(D) } \frac{23}{13} \qquad\text{(E) 2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.