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Problem 120: (2001 AMC 12, 22)
In rectangle $ABCD$, points $F$ and $G$ lie on $AB$ so that $AF=FG=GB$ and $E$ is the midpoint of $\overline{DC}$. Also, $\overline{AC}$ intersects $\overline{EF}$ at $H$ and $\overline{EG}$ at $J$. The area of the rectangle $ABCD$ is $70$. Find the area of triangle $EHJ$. $\text{(A) }\frac {5}{2} \qquad$ $ \text{(B) }\frac {35}{12} \qquad$ $ \text{(C) }3 \qquad$ $ \text{(D) }\frac {7}{2} \qquad$ $ \text{(E) }\frac {35}{8}$
Solution
Exercise 120: Solution
In rectangle $ABCD$, points $F,G$ lie on $\overline{AB}$ so that $AF=GB=\frac14AB$, and $E$ is the midpoint of $\overline{DC}$. Also, $\overline{AC}$ intersects $\overline{EF}$ at $H$ and $\overline{EG}$ at $J$. The area of rectangle $ABCD$ is $75$. Find the area of triangle $EHJ$.
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