Problem 283

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Problem 283: (2005 AMC 10b, 23)

In trapezoid $ABCD$ we have $\overline{AB}$ parallel to $\overline{DC}$, $E$ as the midpoint of $\overline{BC}$, and $F$ as the midpoint of $\overline{DA}$. The area of $ABEF$ is twice the area of $FECD$. What is $AB/DC$?

$\mathrm{(A)} 2 \qquad$ $ \mathrm{(B)} 3 \qquad$ $ \mathrm{(C)} 5 \qquad$ $ \mathrm{(D)} 6 \qquad$ $ \mathrm{(E)} 8$

Solution

Exercise 283: Solution

In trapezoid $ABCD$ we have $\overline{AB}$ parallel to $\overline{DC}$, $E$ as the midpoint of $\overline{BC}$, and $F$ as the midpoint of $\overline{DA}$. The area of $ABEF$ is $1.5$ times the area of $FECD$. What is $AB/DC$?

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