Problem #91: Short Roads

There are four main towns in Lateralia. We will call them A, B, C and D. They lie at the corners of a ten-mile square. In order to improve communications between the towns, the Lateralian Department of Transport decided to build a new road linking all four towns together. Because they had very little money, it was decided that the new road system should be as short as possible and still allow access from any one town to any other. The engineers came up with three designs shown below.
	A______B    A______B    A      B
	|      |    |      |      \  /
	|      |    |      |       \/
	|      |    |      |       /\
	|______|    |      |      /  \
	C      D    C      D    C      D

Number one uses 40 miles of road, number two uses 30 miles of road, and number three uses 28.3 miles of road. The designers naturally recommend plan number three because it employed the smallest road area and, therefore, cost the least. However, when they submitted their plan to the Minister of Finance, he accused them of extravagance and quickly pointed out a better design that required even less total road surface. What was his superior solution?
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