2013 AMC 10A Problems/Problem 15

Problem

Two sides of a triangle have lengths $10$ and $15$ . The length of the altitude to the third side is the average of the lengths of the altitudes to the two given sides. How long is the third side?

$\textbf{(A)}\ 6 \qquad\textbf{(B)}\ 8 \qquad\textbf{(C)}\ 9 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 18$

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2013 AMC 10A Problems/Problem 15

Problem

Solution