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) |
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