2004 Cayley Problem 9

Two vertical towers, AB and CD, are located 16 m apart on flat ground, as shown. Tower AB is 18 m tall and tower CD is 30 m tall. Ropes are tied from A to C and from B to C. Assuming the ropes are taut, the total length of rope, in m, is

\textbf{(A)}\ 54\quad \textbf{(B)}\ 64\quad \textbf{(C)}\ 44\quad \textbf{(D)}\ 48\quad \textbf{(E)}\ 59

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.