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If a rectangle $ABCD$ is cut into four triangles of equal area by lines $AF$, $AG$ and $FG$,where point $F$ is on $BC$ and $G$ is on $CD$, what is $BF$ and $DG$ interms of $BC$ and $CD$ respectively?

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1 Answer

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This is a trick question.

In order for $\Delta ABF$ to have $\frac14$ of the area of the rectangle, we need $F$ to be the midpoint of $BC$. Likewise, we need $G$ to be the midpoint of $CD$. But then $\Delta FCG$ has only $\frac18$ of the area of the rectangle!

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