Question

A, B, C, and D are four villages with a distance of 8 km each making a perfect square. No road exists now. Govt has alloted money to construct road connecting all four villages. But the money is just sufficient for constructing 22 km of road only.How can the road be constructed connecting the four villages with the available money ?​

Answer 1

Given:

A B C and D are the towns in square form with side of 8 km.

To find:

Way to construct the road of 22 km to connect the towns A B C and D.

Solution:

1)We know that the perimeter of the square is 32 km so we can't construct the road along the circumference of the square as this will beyond the project.

2) So we will construct the road under the squared area of the given four towns A B C and D.

3) The correct and systematic construction of the project road given in the attached picture please go through it.

4) In the figure if we construct the 5 Km road under it then we will get the Pythagorean triplet of (3,4,5) So in between the two triangles there must be the road of 2 km which connect all the four towns completely.

There will be only five roads of 5km, 5km, 5km, 5km and 2 km which complete the project road of 22 km.