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 ? (total length of road to be 22 km or less)
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Given:
ABCD is a square with 8 km side.
To find:
Way to construct the road of 22 km to connect the towns.
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.
2) So we will construct the road under the squared area of the towns.
3) The correct and systematic construction 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 them.
Hence there will be five roads 5km, 5km, 5km, 5km and 2 km which makes the project road of 22 km.
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