In triangle $DEF$, angle $F$ is a right angle. Point $G$ lies on $DE$, point $H$ lies on $EF$, and $GH$ is parallel to $DF$. If the length of $DF$ is 80 units, the length of $GH$ is 30 units, and the area of triangle $DEF$ is 1200 square units, what is the length of $HF$, in units?