question_answer

Ravi travelled 4 km straight toward South. He turned left and travelled 6 km straight, then turned right and travelled 4 km straight. How far is he from the starting point?

A)  8 km                           

B)  10 km

C)  12 km             

D)  18 km

Correct Answer: B

Solution :

[b] According to the questions, the direction diagram will be as follow

O is the mid-point of BC and AD.

\[AB=CD=4\text{ }km\]and \[BC=6\text{ }km\]

\[OB=OC=\frac{6}{2}=3\,km\,\]            \[AO=OD\]

\[AO=\sqrt{{{(AB)}^{2}}+{{(OB)}^{2}}}=\sqrt{{{(4)}^{2}}+{{(3)}^{2}}}\]

\[=\sqrt{16+9}=\sqrt{25}=5\,\,km\]

\[\therefore \] Required distance,

\[AD=AO+OD\]

\[=AO+AO=2\times AO\]

\[=2\times 5=10\,\,km\]

(\[AO=OD\] as O is the mid-point of AD)