Triangle $PQR$ is similar to triangle $DEF$, where $P,Q$, and $R$ correspond to $D,E$, and $F$, respectively. In triangle $PQR$, the length of $\overline{PQ}$ is 12 and the length of $\overline{QR}$ is 18. In triangle $DEF$, the length of $\overline{EF}$ is 27. What is the length of $\overline{DE}$?