Difference between revisions of "2010 AMC 12A Problems/Problem 3"
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== Problem 3 == | == Problem 3 == | ||
Rectangle <math>ABCD</math>, pictured below, shares <math>50\%</math> of its area with square <math>EFGH</math>. Square <math>EFGH</math> shares <math>20\%</math> of its area with rectangle <math>ABCD</math>. What is <math>\frac{AB}{AD}</math>? | Rectangle <math>ABCD</math>, pictured below, shares <math>50\%</math> of its area with square <math>EFGH</math>. Square <math>EFGH</math> shares <math>20\%</math> of its area with rectangle <math>ABCD</math>. What is <math>\frac{AB}{AD}</math>? | ||
+ | |||
+ | <center><asy> | ||
+ | unitsize(1mm); | ||
+ | defaultpen(linewidth(.8pt)); | ||
+ | |||
+ | draw((0,0)--(0,25)--(25,25)--(25,0)--cycle); | ||
+ | fill((0,20)--(0,15)--(25,15)--(25,20)--cycle,gray); | ||
+ | draw((0,15)--(0,20)--(25,20)--(25,15)--cycle); | ||
+ | draw((25,15)--(25,20)--(50,20)--(50,15)--cycle); | ||
+ | </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 19:37, 12 February 2010
Problem 3
Rectangle , pictured below, shares
of its area with square
. Square
shares
of its area with rectangle
. What is
?
![[asy] unitsize(1mm); defaultpen(linewidth(.8pt)); draw((0,0)--(0,25)--(25,25)--(25,0)--cycle); fill((0,20)--(0,15)--(25,15)--(25,20)--cycle,gray); draw((0,15)--(0,20)--(25,20)--(25,15)--cycle); draw((25,15)--(25,20)--(50,20)--(50,15)--cycle); [/asy]](http://latex.artofproblemsolving.com/7/2/a/72a3e4616b10c94b9b6fb29e953f9ce742a65ed8.png)
Solution
Let , let
, and let
.