Minimum Road Network Length
XAT 2013 · Quantitative Ability & Data Interpretation · Medium · Geometry
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?
- A.
26.64 km
- B.
27.32 km
- C.
28.30 km
- D.
30 km
- E.
36 km
C
Explanation
Connecting the four vertices of a square of side 10 km via diagonal roads gives length km.
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