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Square and Triangle

Source: 1964 AHSME Problem 10

September 12, 2012
geometryAMC

Problem Statement

Given a square side of length ss. On a diagonal as base a triangle with three unequal sides is constructed so that its area equals that of the square. The length of the altitude drawn to the base is:
<spanclass=′latex−bold′>(A)</span> s2<spanclass=′latex−bold′>(B)</span> s/2<spanclass=′latex−bold′>(C)</span> 2s<spanclass=′latex−bold′>(D)</span> 2s<spanclass=′latex−bold′>(E)</span> 2/s{{ <span class='latex-bold'>(A)</span>\ s\sqrt{2} \qquad<span class='latex-bold'>(B)</span>\ s/\sqrt{2} \qquad<span class='latex-bold'>(C)</span>\ 2s \qquad<span class='latex-bold'>(D)</span>\ 2\sqrt{s} }\qquad<span class='latex-bold'>(E)</span>\ 2/ \sqrt{s} }
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