question_answer

Arun travels 2 km towards East and then he turns to South and travels 4 km. Again he turns to East and travels 4 km, after this he turns to North and travels 12 km. Now, how far is he from his initial point?

A)  \[15\,km\]                    

B)  \[8\,km\]

C)  \[10\,km\] 

D)  \[14\,km\]

Correct Answer: C

Solution :

Let B be the initial point. \[\because \,\,\,ef=4\,km;\,\,\,\therefore \,CD=4\,km\]             \[BD=(BC+CD)\]             \[BD=(2+4)km=6km\Rightarrow AD=8km\] Applying Pythagoras Theorm in \[\Delta ADB\] \[A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\Rightarrow A{{B}^{2}}={{8}^{2}}+{{6}^{2}}\] \[AB=\sqrt{64+36}\Rightarrow AB=10\,km\] So, Arun is \[\] far away from his initial point.