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Simran walks 5 m towards east, turns south and walks 12 m. How far is she from her starting point?
13 m
17 m
7 m
10 m
13 m
Apply the Pythagorean theorem for right-angled triangles: square root of (Base squared + Height squared) where 5 and 12 are the sides, identifying the 5-12-13 Pythagorean triplet.
Apply the Pythagorean theorem for right-angled triangles: square root of (Base squared + Height squared) where 5 and 12 are the sides, identifying the 5-12-13 Pythagorean triplet.
Visualize the Movement
Simran starts at a point, walks 5 m East (horizontal distance), then turns 90 degrees South and walks 12 m (vertical distance).
Form a Right-Angled Triangle
The starting point, the turning point, and the final destination form a right-angled triangle where the hypotenuse represents the distance from the start.
Apply Pythagoras Theorem
Distance = square root of (5┬▓ + 12┬▓) = square root of (25 + 144) = square root of 169 = 13 m.
B: 17 is the sum of distances (5+12) rather than the displacement; C: 7 is the difference of distances (12-5); D: 10 is an incorrect calculation not derived from the geometry.
A is correct because the shortest distance from the start to the end forms the hypotenuse of a right-angled triangle with sides 5 and 12, resulting in 13 m.
Memorize common Pythagorean triplets like 3-4-5, 5-12-13, and 8-15-17 to solve direction problems in seconds without doing manual square root calculations.
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