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A man walks 4 km towards East, then turns left and walks 3 km. How far is he from the starting point?
5 km
7 km
6 km
4 km
5 km
Recognize the standard Pythagorean triplet 3-4-5. Since the path forms a right-angled triangle with legs of 4 km and 3 km, the hypotenuse must be 5 km.
Recognize the standard Pythagorean triplet 3-4-5. Since the path forms a right-angled triangle with legs of 4 km and 3 km, the hypotenuse must be 5 km.
Visualize the path
The man starts at a point, walks 4 km East (base), and then turns left (North) to walk 3 km (height). This creates a right-angled triangle where the displacement is the hypotenuse.
Apply Pythagoras Theorem
Using the formula c squared = a squared + b squared, where a = 4 and b = 3. So, c squared = 4 squared + 3 squared = 16 + 9 = 25. The distance c = square root of 25 = 5 km.
B: 7 km is the sum of the distances (4+3), representing total distance walked, not displacement. C: 6 km is mathematically incorrect based on the Pythagorean theorem. D: 4 km is merely one of the two legs walked and ignores the second leg.
A is correct because the shortest distance from the starting point to the final position is the hypotenuse of a right-angled triangle with sides 4 km and 3 km, which is 5 km.
Whenever you see right-angle turns, look for common Pythagorean triplets like 3-4-5, 5-12-13, or 8-15-17 to solve distance problems instantly without complex calculations.
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