Shortest road from village to QR

Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road? Note: The figure shown is representative. Figure: triangle with P at the top, Q at the bottom-left and R at the bottom-right; PQ = 13 km and PR = 15 km are dashed, QR = 14 km is solid.