2003 Cayley Problem 23

A pyramid has a square base which has an area of 1440 cm^2. Each of the pyramid's triangular faces is identical and each has an area of 840 cm^2. The height of the pyramid, in cm, is

\textbf{(A)}\ 30\sqrt{2}\quad \textbf{(B)}\ 40\quad \textbf{(C)}\ 20\sqrt{6}\quad \textbf{(D)}\ 20\sqrt{3}\quad \textbf{(E)}\ 30

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.