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An altitude problem

Source: AHSME 1986 problem 29

October 2, 2011
inequalitiescalculusintegrationtriangle inequalityAMC

Problem Statement

Two of the altitudes of the scalene triangle ABCABC have length 44 and 1212. If the length of the third altitude is also an integer, what is the biggest it can be?
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> none of these <span class='latex-bold'>(A)</span>\ 4\qquad<span class='latex-bold'>(B)</span>\ 5\qquad<span class='latex-bold'>(C)</span>\ 6\qquad<span class='latex-bold'>(D)</span>\ 7\qquad<span class='latex-bold'>(E)</span>\ \text{none of these}
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