1955 AHSME Problem 21

Represent the hypotenuse of a right triangle by c and the area by A. The altitude on the hypotenuse is:

\textbf{(A)}\ \frac{A}{c}\qquad\textbf{(B)}\ \frac{2A}{c}\qquad\textbf{(C)}\ \frac{A}{2c}\qquad\textbf{(D)}\ \frac{A^2}{c}\qquad\textbf{(E)}\ \frac{A}{c^2}

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