I was tutoring a student today and one of the practice problems we were working on asked the question posed in the title, including an image like the one below. The quadrilaterals each represent a car in a train in a perspective sketch with the triangle CDE representing all of the following cars to the vanishing point on the horizon. The triangles in question
After looking at the problem, neither of us could see how to find the length of EF with the given information and we moved on. Is there a solution that we missed or is this problem just missing information?
We need to apply the the intercept theorem (a.k.a Thales' Theorem) three times. First, $$\frac{1.9}{8.4}=\frac{EF}{FG}=\frac{1.9k}{8.4k}$$ Now, focus on $\bigtriangleup DBF$ to find CD in terms of $K$. $$\frac{5.4}{1.9k}=\frac{CD}{BC}=\frac{\frac{5.4}{k}}{1.9} \implies CD=\frac{5.4}{k}$$ Finally, focus on $\bigtriangleup ADG$ to find $k$.
$$\frac{\frac{5.4}{k}+1.9}{8.4}=\frac{5.4+1.9k}{8.4k}$$
I believe $k$ turns out to be exactly $1$ and hence, $EF=1.9$ units.