A school, a hospital, and a supermarket are located at the intersections of three highways. The highways intersect to form a right triangle. The school and the hospital are 14.7 miles apart. The distance between the school and the supermarket is 8.82 miles, and the distance from the hospital to the supermarket is 11.76 miles. A service road is going to be constructed from the highway that connects the school and the hospital to the back entrance of the supermarket. What is the shortest possible distance for the service road. Round your answer to the nearest tenth of a mile miles