Difference between revisions of "2012 AMC 12B Problems/Problem 21"

(Created page with "==Problem== Square <math>AXYZ</math> is inscribed in equiangular hexagon <math>ABCDEF</math> with <math>X</math> on <math>\overline{BC}</math>, <math>Y</math> on <math>\overline...")
 
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<math> \textbf{(A)}\ 29\sqrt{3} \qquad\textbf{(B)}\ \frac{21}{2}\sqrt{2}+\frac{41}{2}\sqrt{3}\qquad\textbf{(C)}\ 20\sqrt{3}+16</math>
 
<math> \textbf{(A)}\ 29\sqrt{3} \qquad\textbf{(B)}\ \frac{21}{2}\sqrt{2}+\frac{41}{2}\sqrt{3}\qquad\textbf{(C)}\ 20\sqrt{3}+16</math>
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<math>\textbf{(D)}\ 20\sqrt{2}+13\sqrt{3}  
 
<math>\textbf{(D)}\ 20\sqrt{2}+13\sqrt{3}  
 
\qquad\textbf{(E)}\ 21\sqrt{6}</math>
 
\qquad\textbf{(E)}\ 21\sqrt{6}</math>

Revision as of 23:20, 24 February 2012

Problem

Square $AXYZ$ is inscribed in equiangular hexagon $ABCDEF$ with $X$ on $\overline{BC}$, $Y$ on $\overline{DE}$, and $Z$ on $\overline{EF}$. Suppose that $AB=40$, and $EF=41(\sqrt{3}-1)$. What is the side-length of the square?

$\textbf{(A)}\ 29\sqrt{3} \qquad\textbf{(B)}\ \frac{21}{2}\sqrt{2}+\frac{41}{2}\sqrt{3}\qquad\textbf{(C)}\ 20\sqrt{3}+16$

$\textbf{(D)}\ 20\sqrt{2}+13\sqrt{3}  \qquad\textbf{(E)}\ 21\sqrt{6}$

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