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2013 AMC 10B Problems/Problem 15

Revision as of 18:02, 21 February 2013 by Turkeybob777 (talk | contribs) (Created page with "A wire is cut into two pieces, one of length <math>a</math> and the other of length <math>b</math>. The piece of length <math>a</math> is bent to form an equilateral triangle, an...")
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A wire is cut into two pieces, one of length $a$ and the other of length $b$. The piece of length $a$ is bent to form an equilateral triangle, and the piece of length $b$ is bent to form a regular hexagon. The triangle and the hexagon have equal area. What is $\frac{a}{b}$?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ \frac{\sqrt{6}}{2}\qquad\textbf{(C)}\ \sqrt{3} \qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{3\sqrt{2}}{2}$

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