1953 AHSME Problem 26

The base of a triangle is 15 inches. Two lines are drawn parallel to the base, terminating in the other two sides, and dividing the triangle into three equal areas. The length of the parallel closer to the base is:

\begin{array}{l} \textbf{(A)}\ 5\sqrt{6}\text{ inches} \qquad \textbf{(B)}\ 10\text{ inches} \qquad \textbf{(C)}\ 4\sqrt{3}\text{ inches}\qquad \textbf{(D)}\ 7.5\text{ inches}\\ \textbf{(E)}\ \text{none of these} \end{array}

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