A regional airport, community college, and city hall building are located at the vertices of a right triangle formed by three roads. The airport and the city hall are 10 miles apart.
The distance between the airport and the community college is 8 miles, and the distance
between the city hall and the community college is 6 miles,
A service road will be constructed from the main entrance of the community college to
the road that connects the airport and the city hall. What is the shortest possible length
for the service road Round your answer to the nearest tenth,