Question : Direction: A man travels 4 kilometres due north, then travels 6 kilometres due east, and further travels 4 kilometres due north. How far is he from the starting point?
Option 1: 8 km
Option 2: 10 km
Option 3: 6 km
Option 4: 14 km
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Correct Answer: 10 km
Solution : As per the given information, the movement of the man looks as follows –
The direct distance between his starting point and the endpoint is AD as shown below –
Produce DC to O and join AO to form a right-angled triangle at O, with AD as hypotenuse, AO as base, and DO as perpendicular.
According to the rectangular properties, i.e., opposite sides are equal, so, AO = 6 km, CO = 4 km ⇒ DO = 8 km.
In right-angled triangle AOD, use Pythagoras theorem,
(Hypotenuse) 2 = (Perpendicular) 2 + (Base) 2
(AD) 2 = (DO) 2 + (AO) 2
(AD) 2 = 8 2 + 6 2
(AD) 2 = 64 + 36 ⇒ (AD) 2 = 100 ⇒ AD = (100) ½
AD = 10
Distance between his starting point and the endpoint = 10 km .
Hence, the second option is correct.
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