AHSME 1967 Problem 37

Segments $AD=10$, $BE=6$, $CF=24$ are drawn from the vertices of triangle $ABC$, each perpendicular to a straight line $RS$, not intersecting the triangle. Points $D$, $E$, $F$ are the intersection points of $RS$ with the perpendiculars. If $x$ is the length of the perpendicular segment $GH$ drawn to $RS$ from the intersection point $G$ of the medians of the triangle, then $x$ is: $\textbf{(A)}\ \frac{40}{3} \textbf{(B)}\ 16 \textbf{(C)}\ \frac{56}{3} \textbf{(D)}\ \frac{80}{3} \textbf{(E)}\ \text{undetermined}$