Difference between revisions of "2010 AMC 12A Problems/Problem 3"
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<center><asy> | <center><asy> | ||
unitsize(1mm); | unitsize(1mm); | ||
− | defaultpen(linewidth(.8pt)); | + | defaultpen(linewidth(.8pt)+fontsize(8pt)); |
draw((0,0)--(0,25)--(25,25)--(25,0)--cycle); | draw((0,0)--(0,25)--(25,25)--(25,0)--cycle); | ||
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draw((0,15)--(0,20)--(25,20)--(25,15)--cycle); | draw((0,15)--(0,20)--(25,20)--(25,15)--cycle); | ||
draw((25,15)--(25,20)--(50,20)--(50,15)--cycle); | draw((25,15)--(25,20)--(50,20)--(50,15)--cycle); | ||
+ | |||
+ | label("$A$",(0,20),W); | ||
+ | label("$B$",(50,20),E); | ||
+ | label("$C$",(50,15),E); | ||
+ | label("$D$",(0,15),W); | ||
+ | label("$E$",(0,25),NW); | ||
+ | label("$F$",(25,25),NE); | ||
+ | label("$G$",(25,0),SE); | ||
+ | label("$H$",(0,0),SW); | ||
</asy></center> | </asy></center> | ||
+ | |||
<math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 10</math> | <math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 10</math> |
Revision as of 18:41, 12 February 2010
Problem 3
Rectangle , pictured below, shares of its area with square . Square shares of its area with rectangle . What is ?
Solution
Let , let , and let .