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A man walks 6 km East, turns right and walks 8 km. What is the shortest distance from his starting point?
10 km
12 km
14 km
7 km
10 km
Apply the Pythagorean theorem for right-angled triangles: the shortest distance is the square root of (Base squared + Height squared).
Apply the Pythagorean theorem for right-angled triangles: the shortest distance is the square root of (Base squared + Height squared).
Visualize Movement
The man walks 6 km East (horizontal base) and turns right to walk 8 km South (vertical height). This forms a right-angled triangle where the starting point and ending point form the hypotenuse.
Apply Pythagoras Theorem
Let the horizontal distance be a=6 and vertical distance be b=8. The shortest distance (hypotenuse c) is calculated as c = sqrt(a squared + b squared) = sqrt(6 squared + 8 squared) = sqrt(36 + 64) = sqrt(100).
Calculate Result
The square root of 100 is 10. Thus, the shortest distance from the starting point is 10 km.
B: 12 km is incorrect as it does not satisfy the geometric square root calculation. C: 14 km is the sum of the distances (6+8) which represents total path covered, not the shortest distance. D: 7 km is numerically incorrect based on the Pythagorean triplet 6-8-10.
A is correct because the shortest path forms a right-angled triangle with sides 6 and 8, resulting in a hypotenuse of 10 km.
Always memorize common Pythagorean triplets like 3-4-5, 6-8-10, and 5-12-13 to solve distance problems instantly without formal calculation.