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A person walks 5m North, turns East and walks 12m. How far is he from the starting point?
13m
17m
7m
15m
13m
Recognize the Pythagorean triple 5-12-13, which forms the hypotenuse of the right-angled triangle created by the North and East movements.
Recognize the Pythagorean triple 5-12-13, which forms the hypotenuse of the right-angled triangle created by the North and East movements.
Visualize the Movement
The person moves 5m North (vertical displacement) and then 12m East (horizontal displacement), creating a right-angled triangle where the starting point to the current position is the hypotenuse.
Apply Pythagoras Theorem
According to the theorem, hypotenuse squared = base squared + height squared. So, Distance = sqrt(5 squared + 12 squared) = sqrt(25 + 144) = sqrt(169).
Calculate Result
The square root of 169 is 13. Therefore, the direct distance from the starting point is 13 meters.
B: 17m is the sum of the distances (5+12) rather than the displacement; C: 7m is the difference of the distances (12-5); D: 15m is a common distractor that does not follow the Pythagorean geometry.
A is correct because the displacement forms the hypotenuse of a right-angled triangle with sides 5m and 12m, which equals 13m.
Always memorize common Pythagorean triples like 3-4-5, 5-12-13, and 8-15-17 to solve distance-based direction questions instantly without manual calculation.
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