1950 AHSME Problem 47

A rectangle inscribed in a triangle has its base coinciding with the base b of the triangle. If the altitude of the triangle is h, and the altitude x of the rectangle is half the base of the rectangle, then:

\begin{array}{l} \textbf{(A)}\ x=\frac{1}{2}h\qquad\textbf{(B)}\ x=\frac{bh}{b+h}\qquad\textbf{(C)}\ x=\frac{bh}{2h+b}\qquad\textbf{(D)}\ x=\sqrt{\frac{hb}{2}}\qquad\\ \textbf{(E)}\ x=\frac{1}{2}b \end{array}

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