Problem 249

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Problem 249: (2009 AMC 10a, 17)

Rectangle $ABCD$ has $AB=4$ and $BC=3$. Segment $EF$ is constructed through $B$ so that $EF$ is perpendicular to $DB$, and $A$ and $C$ lie on $DE$ and $DF$, respectively. What is $EF$? $\mathrm{(A)}\ 9 \qquad$ $ \mathrm{(B)}\ 10 \qquad$ $ \mathrm{(C)}\ \frac {125}{12} \qquad$ $ \mathrm{(D)}\ \frac {103}{9} \qquad$ $ \mathrm{(E)}\ 12$

Solution

Exercise 249: Solution

Rectangle $ABCD$ has $AB=12$ and $BC=5$. Segment $EF$ is constructed through $B$ so that $EF$ is perpendicular to $DB$, and $A$ and $C$ lie on $DE$ and $DF$, respectively. What is $EF$?

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