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Ratio of areas

Source: AHSME 1963 Problem 15

January 9, 2014
ratiogeometryAMC

Problem Statement

A circle is inscribed in an equilateral triangle, and a square is inscribed in the circle. The ratio of the area of the triangle to the area of the square is:
<spanclass=′latex−bold′>(A)</span> 3:1<spanclass=′latex−bold′>(B)</span> 3:2<spanclass=′latex−bold′>(C)</span> 33:2<spanclass=′latex−bold′>(D)</span> 3:2<spanclass=′latex−bold′>(E)</span> 3:22<span class='latex-bold'>(A)</span>\ \sqrt{3}:1 \qquad <span class='latex-bold'>(B)</span>\ \sqrt{3}:\sqrt{2} \qquad <span class='latex-bold'>(C)</span>\ 3\sqrt{3}:2 \qquad <span class='latex-bold'>(D)</span>\ 3:\sqrt{2} \qquad <span class='latex-bold'>(E)</span>\ 3:2\sqrt{2}
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