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In the country of Four, there are four cities, A, B, C and D. B is to the East of A, C is to the South of B, D is to the West of C, and A is to the North of D. The Government of Four is planning to connect these four cities by road such that it is possible for a person to go from a city to any of the other three cities. At the same time, the Government wants to ensure that the total road length is minimum. The distances between A to B, B to C, C to D and D to A are all equal to 10 km. What should be the total length of the road?
We can draw the towns as shown in the diagram below.
For the minimum length the Government should diagonal roads. The length of road will be same as the length of a diagonal of a square whose side length is 10 km.
Length of one diagonal = $$\sqrt{2}*10$$ = 1.414*10 = 14.14 km
Therefore, total length of both the roads = 2*14.14 $$\approx$$ 28.30 km.
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