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A man walks 5km East, then turns South and walks 12km. How far is he from the starting point?
13km
15km
17km
19km
13km
Recognize the Pythagorean triple (5, 12, 13) to calculate the displacement instantly without manual arithmetic.
Recognize the Pythagorean triple (5, 12, 13) to calculate the displacement instantly without manual arithmetic.
Visualize the path
The man travels 5km East (along the X-axis) and then 12km South (along the Y-axis). This forms a right-angled triangle where the legs are 5km and 12km.
Apply Pythagoras Theorem
The distance from the starting point is the hypotenuse of the right-angled triangle. Hypotenuse = square root of (base squared + height squared) = square root of (5 squared + 12 squared) = square root of (25 + 144) = square root of 169 = 13km.
B: 15km is mathematically incorrect as it does not satisfy the square root of (5 squared + 12 squared). C: 17km is the sum of the distances (5+12) rather than the displacement. D: 19km is an arbitrary value inconsistent with the geometry of the movement.
A is correct because the displacement forms the hypotenuse of a right-angled triangle with sides 5 and 12, resulting in exactly 13km.
Always look for common Pythagorean triples like (3,4,5), (5,12,13), and (8,15,17) in direction problems to save time on manual calculations.
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