2005 AMC 10B Problems/Problem 23

Revision as of 20:55, 23 August 2011 by Baijiangchen (talk | contribs) (Solution)

Problem

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

The length of $EF$ is the arithmetic mean of the two parallel bases. Since the base EF is shared between the two smaller trapezoids, you want AB/DC = \boxed{2}$.

See Also