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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


Team Careers360 11th Jan, 2024
Answer (1)
Team Careers360 20th Jan, 2024

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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