A) \[3x\,km\]
B) \[3\sqrt{2}x\,\text{km}\]
C) \[2(\sqrt{2}+1)x\,\text{km}\]
D) \[2\sqrt{2}\,x\,\text{km}\]
Correct Answer: A
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 \[OD=\sqrt{{{(2\sqrt{2}\cdot x)}^{2}}+{{x}^{2}}}\] \[=\sqrt{8{{x}^{2}}+{{x}^{2}}}=3x\ \text{km}\]You need to login to perform this action.
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