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Square and Equilateral Triangle

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February 17, 2008
geometryperimeterarea of a triangle

Problem Statement

A square and an equilateral triangle have the same perimeter. Let A A be the area of the circle circumscribed about the square and B B be the area of the circle circumscribed about the triangle. Find A/B A/B. <spanclass=′latex−bold′>(A)</span> 916<spanclass=′latex−bold′>(B)</span> 34<spanclass=′latex−bold′>(C)</span> 2732<spanclass=′latex−bold′>(D)</span> 368<spanclass=′latex−bold′>(E)</span> 1 <span class='latex-bold'>(A)</span>\ \frac{9}{16} \qquad <span class='latex-bold'>(B)</span>\ \frac{3}{4} \qquad <span class='latex-bold'>(C)</span>\ \frac{27}{32} \qquad <span class='latex-bold'>(D)</span>\ \frac{3\sqrt{6}}{8} \qquad <span class='latex-bold'>(E)</span>\ 1
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