2002 Fermat Problem 25

The lengths of all six edges of a tetrahedron are integers. The lengths of five of the edges are 14, 20, 40, 52, and 70. The number of possible lengths for the sixth edge is

\textbf{(A)}\ 9\quad \textbf{(B)}\ 3\quad \textbf{(C)}\ 4\quad \textbf{(D)}\ 5\quad \textbf{(E)}\ 6

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

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