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Problem Description Two of the altitudes of the scalene triangle \(ABC\) have length \(4\) and \(12\). If the length of the third altitude is also an integer, what is the biggest it can be? $$ \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ \text{none of these} $$

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Solution B

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