A house is located at each corner of a square with side lengths of 13 mi. What is the length of the shortest road system with straight roads that connects all of the houses by roads (that is, a road system that allows one to drive from any house to any other house)? (Hint: Place two points, P and Q, above the midpoint of the base of the square, at distance x from the lower and upper sides of the square, respectively)
The length of the shortest road system is $oxed{}$ mi.
(Type an exact answer, using radicals as needed)