A man walks 5 kms East, then takes a right turn and walk 12 kms. How far is he…

Concept: when a path includes a turn, the straight-line distance (displacement) between the start and end points equals the hypotenuse of the right triangle formed by the two path segments, whenever those two segments are perpendicular to each other — displacement = √(leg12 + leg22), not the sum of the leg lengths.

1. The man first walks 5 km East — this is the first leg of the path.

2. He then takes a right turn. Facing East, a right turn means he now faces South, so he walks 12 km South — this second leg is perpendicular to the first.

3. Since the two legs are perpendicular, they form a right-angled triangle with legs 5 km and 12 km, and the straight-line distance from the starting point is the hypotenuse of this triangle.

4. distance = √(52 + 122) = √(25 + 144) = √169 = 13 km.

Cross-check: 5-12-13 is a well-known Pythagorean triple, since 52 + 122 = 25 + 144 = 169 = 132, independently confirming the result.

So the man is 13 km from his starting point.