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Time and Distance Practice Test 1 with solutions

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Question : 25 of 40

Marks: +1, -0

In the country of Four, there are four cities named, 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 plan to connect these four cities by road such that it is possible for a person to go from one 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?

26.64 km
27.32 km
28.30 km
30 km
36 km

Solution: 👈: Video Solution

By Pythagoras theorm,

AC^2

=

AD^2 + DC^2

AC^2

=

(10)^2 + (10)^2

AC^2

= 100 + 100

AC = 10

\sqrt{2}

km.

or BD = 10

\sqrt{2}

km

Total distance = 20

\sqrt{2}

= 20 × 1.414

= 28.28 km.

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