AHSME 1962 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: $\textbf{(A)}\ \frac{9}{2} \textbf{(B)}\ 2\sqrt{5} \textbf{(C)}\ 4\sqrt{2} \textbf{(D)}\ \frac{9\sqrt{2}}{2} \textbf{(E)}\ \text{none of these}$