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P29 [Geometry] - Turkish NMO 1st Round - 2005

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October 26, 2013
geometrytrigonometry

Problem Statement

Let h1h_1 and h2h_2 be the altitudes of a triangle drawn to the sides with length 55 and 262\sqrt 6, respectively. If 5+h1≤26+h25+h_1 \leq 2\sqrt 6 + h_2, what is the third side of the triangle?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 26<spanclass=′latex−bold′>(D)</span> 36<spanclass=′latex−bold′>(E)</span> 53 <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 7 \qquad<span class='latex-bold'>(C)</span>\ 2\sqrt 6 \qquad<span class='latex-bold'>(D)</span>\ 3\sqrt 6 \qquad<span class='latex-bold'>(E)</span>\ 5\sqrt 3
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