Three villages $P, Q$, and $R$ are located in such a way that the distance $P Q=13 \mathrm{~km}$, $Q R=14 \mathrm{~km}$, and $R P=15 \mathrm{~km}$, as shown in the figure. A straight road joins $Q$ and $R$. It is proposed to connect $P$ to this road $Q R$ by constructing another road. What is the minimum possible length (in km ) of this connecting road?

Note: The figure shown is representative.