A) \[(2\times \sqrt{2}+1)x\,\,km\]
B) \[3x\,\,km\]
C) \[2\sqrt{2}x\,\,km\]
D) \[3\sqrt{2}x\,\,km\]
Correct Answer: B
Solution :
In\[\Delta BCD,\] \[B{{D}^{2}}=B{{C}^{2}}+C{{D}^{2}}={{x}^{2}}+{{x}^{2}}\] \[\Rightarrow \] \[BD=\sqrt{2}x\] \[\Rightarrow \] \[BD=AE=\sqrt{2}x\] \[\therefore \] \[OE=OA+AE=\sqrt{2}\cdot x+\sqrt{2}\cdot x=2\sqrt{2}x\] \[\because \] \[BA=DE=x\] \[\therefore \]In \[\Delta ODE,\] \[O{{D}^{2}}=O{{E}^{2}}+D{{E}^{2}}\] \[\therefore \]Minimum distance \[\therefore \]\[OD=\sqrt{{{(2\sqrt{2}\cdot x)}^{2}}+{{x}^{2}}}=\sqrt{8{{x}^{2}}+{{x}^{2}}}=3x\,\,km\]You need to login to perform this action.
You will be redirected in
3 sec