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2014 AMC 10B Problem 15

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2014 AMC 10B Problem 15AMC 10 Step by Step

Name: Date: September 13, 2026

Triangles: Area & Pythagorean · difficulty 3 of 5 · about 4 min · position P11-15

In rectangle $ABCD$ , $DC=2 \cdot CB$ and points $E$ and $F$ lie on $\overline{AB}$ so that $\overline{ED}$ and $\overline{FD}$ trisect $\angle ADC$ as shown. What is the ratio of the area of $\triangle DEF$ to the area of rectangle $ABCD$ ?

A)
$\frac{\sqrt{3}}{6}$
B)
$\frac{\sqrt{6}}{8}$
C)
$\frac{3\sqrt{3}}{16}$
D)
$\frac{1}{3}$
E)
$\frac{\sqrt{2}}{4}$

2014 AMC 10B Problem 15

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