In the figure below, $ABCD$ is a parallelogram, $AD=18$ and $DC=27$. Segments $\overline{EG}$ and $\overline{FH}$ are perpendicular to sides

In the figure below, $ABCD$ is a parallelogram, $AD=18$ and $DC=27$. Segments $\overline{EG}$ and $\overline{FH}$ are perpendicular to sides