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Equal Perimeters of a Square and Triangle

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March 2, 2010
geometryperimeter

Problem Statement

A square and an equilateral triangle have equal perimeters. The area of the triangle is 93 9 \sqrt{3} square inches. Expressed in inches the diagonal of the square is: <spanclass=′latex−bold′>(A)</span> 92<spanclass=′latex−bold′>(B)</span> 25<spanclass=′latex−bold′>(C)</span> 42<spanclass=′latex−bold′>(D)</span> 922<spanclass=′latex−bold′>(E)</span> none of these <span class='latex-bold'>(A)</span>\ \frac{9}{2} \qquad <span class='latex-bold'>(B)</span>\ 2 \sqrt{5} \qquad <span class='latex-bold'>(C)</span>\ 4 \sqrt{2} \qquad <span class='latex-bold'>(D)</span>\ \frac{9 \sqrt{2}}{2} \qquad <span class='latex-bold'>(E)</span>\ \text{none of these}
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