1998 Gauss 8 Problem 23

If the sides of a triangle have lengths 30, 40 and 50, what is the length of the shortest altitude?

\textbf{(A)}\ 20\quad \textbf{(B)}\ 24\quad \textbf{(C)}\ 25\quad \textbf{(D)}\ 30\quad \textbf{(E)}\ 40

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