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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