20. In the triangle $F G H$, we can draw a line parallel to its base $F G$, through point $X$ or $Y$. The areas of the shaded regions are the same. The ratio $H X: X F=4: 1$. What is the ratio $H Y: Y F$ ?
A $1: 1$
B $2: 1$
C $3: 1$
D $3: 2$
E $4: 3$
20. D In the triangle on the left, the unshaded triangle is similar to triangle $F G H$, and is obtained from it by a scale factor of $\frac{4}{5}$. Hence its area is $\left(\frac{4}{5}\right)^{2}=\frac{16}{25}$ of the area of $F G H$. The shaded area is therefore $\frac{9}{25}$ of the area of $F G H$. Hence $H Y: H F=3: 5$ and so $H Y: Y F=3: 2$.