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A person walks 5m North, turns East and walks 12m. What is the shortest distance from the starting point?
13m
17m
7m
15m
13m
Recognize the standard Pythagorean triplet (5, 12, 13) to calculate the hypotenuse instantly without formal calculation.
Recognize the standard Pythagorean triplet (5, 12, 13) to calculate the hypotenuse instantly without formal calculation.
Define the path coordinates
Starting at origin (0,0), move 5m North to (0,5). Then, move 12m East to reach (12,5).
Apply Pythagoras Theorem
The shortest distance is the hypotenuse of a right triangle with base 12m and height 5m. Distance = square root of (5┬▓ + 12┬▓) = square root of (25 + 144) = square root of 169 = 13m.
B: 17m is the sum of the distances (5+12), which represents total distance walked, not the shortest displacement. C: 7m is the difference between the distances (12-5), which has no geometric relevance here. D: 15m is an incorrect calculation and does not fit the Pythagorean triplet for these legs.
A is correct because the shortest path forms the hypotenuse of a right-angled triangle with sides 5m and 12m, which equals 13m based on the Pythagorean theorem.
Always check for Pythagorean triplets like (3,4,5), (5,12,13), and (8,15,17) in direction problems to save time on calculations.
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