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Four villages form the vertices of a rectangle of dimensions 8.0 km x 6.0 km. Roads are to be laid connecting the villages such that the distance by r

Question

Four villages form the vertices of a rectangle of dimensions 8.0 km x 6.0 km. Roads are to be laid connecting the villages such that the distance by road between each pair of villages is the same. The shortest such road distance (in km) between any pair of villages will be

10 10√3

10√2

14

Solution

Correct option is A

Given:

Rectangle dimensions: 8 km × 6 km

Formula Used:
Diagonal of rectangle: $\sqrt{\text{length}^2 + \text{width}^2}$

Solution:

$\sqrt{\text{length}^2 + \text{width}^2}\\\ \\ = \sqrt{8^2 + 6^2} = \sqrt{100} = 10$
To make all road distances equal, use:
Shortest equal distance = Diagonal × √3
= 10 × √3

Final Answer: (B) 10√3 km