Difference between revisions of "2010 AMC 12A Problems/Problem 3"
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<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> | ||
| − | + | == Solution == | |
| + | Let <math>EF = FG = GF = HE = s</math>, let <math>AD = BC = h</math>, and let <math>AB = CD = x</math>. | ||
| + | |||
| + | |||
| + | <math>.2s^2 = hs</math> | ||
| + | |||
| + | <math>s = 5h</math> | ||
| + | |||
| + | <math>.5hx = hs</math> | ||
| + | |||
| + | <math>x = 2s = 10h</math> | ||
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| + | |||
| + | <math>\frac{AB}{AD} = \frac{x}{h} = \boxed{10\ \textbf{(E)}}</math> | ||
Revision as of 12:25, 11 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 
.
