1978 AHSME Problem 7

Opposite sides of a regular hexagon are 12 inches apart. The length of each side, in inches, is

\textbf{(A) }7.5\qquad \textbf{(B) }6\sqrt{2}\qquad \textbf{(C) }5\sqrt{2}\qquad \textbf{(D) }\frac{9}{2}\sqrt{3}\qquad \textbf{(E) }4\sqrt{3}

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