All Roads Should Lead
The first proposal is of 40 km length, the second of 30 and the third gives a solution with 28.3 km of road. The designers approved the third plan, but the finance minister sent it back accusing the designers of extravagance. He claimed that a better solution should exist. But, the minister was an old chap and may be wrong.
What is the shortest total length of road that would connect the four towns? Give your answer in metres, approximated to the nearest metre.