Question : Directions: A man walks 10 km in the east direction and then turns to the right and moves 5 km in that direction. Then, he takes a left turn and moves 2 km ahead. Find the minimum distance between his initial and final positions.
Option 1: 12 km
Option 2: 13 km
Option 3: 7 km
Option 4: 18 km
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Correct Answer: 13 km
Solution : Firstly, draw a diagram as per the given instructions –
Now, we have to find the shortest distance –
Apply Pythagoras' theorem to the given triangle, ABC –
(Hypotenuse) 2 = (Perpendicular) 2 + (Base) 2 AC 2 = BC 2 + AB 2 AC 2 = (5) 2 + (10 + 2) 2 AC 2 = (5) 2 + (12) 2 AC 2 = 25 + 144 AC 2 = 169 AC = √ 169 AC = 13 km
So, the shortest distance between the starting and the endpoints is 13 km. Hence, the second option is correct.
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