A) \[200\sqrt{29}\,km\]
B) \[100\sqrt{3}\,km\]
C) \[150\sqrt{34}\,km\]
D) \[250\sqrt{34}\,km\]
Correct Answer: C
Solution :
[c] Distance \[=\text{ Speed}\times \text{Time}\] |
Distance travelled by the aeroplane due north in \[1\frac{1}{2}\] hour |
\[=300\times \frac{3}{2}=450\,km\] |
Distance travelled by the aeroplane due west in \[1\frac{1}{2}\] hour |
\[=500\times \frac{3}{2}=750\,km\] |
In \[\Delta AOB,\] by Pythagoras theorem |
\[A{{B}^{2}}=A{{O}^{2}}+O{{B}^{2}}\] |
\[\Rightarrow \,\,A{{B}^{2}}={{(450)}^{2}}+{{(750)}^{2}}\] |
\[\Rightarrow \,\,A{{B}^{2}}=202500+562500=765000\] |
\[\therefore \,\,\,\,\,AB=\sqrt{765000}\] |
\[=\sqrt{9\times 25\times 34\times 100}=150\sqrt{34}km\] |
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