Golu started from his house towards North. After covering a distance of 8 km,…

Concept: When a path turns through a right angle, the two straight-line segments walked form the two legs of a right triangle. The shortest (straight-line) distance back to the starting point is the hypotenuse of that triangle, found using the Pythagorean theorem: hypotenuse² = (leg 1)² + (leg 2)².

1. Golu walks 8 km North from his house.

2. Facing North, a left turn points him West, so he walks 6 km West.

3. The North leg and the West leg meet at a right angle, so they are the two legs of a right triangle. The straight-line distance from his house to his current position is the hypotenuse of that triangle.

4. Applying the Pythagorean theorem: distance = √(82 + 62) = √(64 + 36) = √100 = 10 km.

Cross-check: 6-8-10 is simply the classic 3-4-5 right-triangle ratio scaled by 2, which confirms the hypotenuse is exactly 10 km.

So the shortest distance from Golu's house is 10 km.