1962 AHSME Problem 6

A square and an equilateral triangle have equal perimeters. The area of the triangle is 9 \sqrt{3} square inches. Expressed in inches the diagonal of the square is:

\textbf{(A)}\ \frac{9}{2} \qquad \textbf{(B)}\ 2 \sqrt{5} \qquad \textbf{(C)}\ 4 \sqrt{2} \qquad \textbf{(D)}\ \frac{9\sqrt{2}}{2}\qquad \textbf{(E)}\ \text{none of these}

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