1952 AHSME Problem 39

If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:

\begin{array}{l} \textbf{(A)}\ \frac {\sqrt {8d^2 - p^2}}{2} \qquad \textbf{(B)}\ \frac {\sqrt {8d^2 + p^2}}{2} \qquad \textbf{(C)}\ \frac{\sqrt{6d^2-p^2}}{2}\qquad\\ \textbf{(D)}\ \frac {\sqrt {6d^2 + p^2}}{2} \qquad \textbf{(E)}\ \frac {8d^2 - p^2}{4} \end{array}

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