Cutting a rectangle into four equal triangles from a corner in rectangle

Question

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?

Answer 1

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!