Four towns are located at the vertices of a 4 mile by 6 mile rectangle. By using three sides of the rectangle, a road network of total length 14 miles can be constructed which connects all four towns. Is there a shorter road network, which connects the towns? Specifically, there is a suitable network of length less that 13 miles.

Hint 1

A crossroads does not have to be in a town; try adding some points to the picture and having roads cross at the new
points

Hint 2

Add two new points inside the rectangle, and find a network with roads branching off at those two points

Here's another hint