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A school, hospital, and a supermarket are located at the vertices of a right triangle formed by three highways. The school and hospital are 14.7 miles apart. The distance between the school and the supermarket is 8.82 miles, and the distance between the hospital and the supermarket is 11.76 miles. A service road will be constructed from the main entrance of the supermarket to the highway that connects the school and hospital. What is the shortest possible length for the service road? Round to the nearest tenth.


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