Question

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?

Answer 1

Answer:

28.30

Explanation:

A  -- B

|        |        

D  -- C

Accoding to the question, ABCD is a square

Minimum length of road = 10 * root(2) + 10 * root(2) = 20 * root(2) = 28.30

Answer 2

Answer:

      The total length of the road is 28.30 km.

Explanation:

         For the minimum length of the government should be diagonal roads.  The length of the road will be the 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, the total length of both roads$=2$×$14.14$

                                                                             $=28.30 km$.