A) \[35\sqrt{2}cm\]
B) \[70\sqrt{2}cm\]
C) \[\frac{35\sqrt{3}}{2}cm\]
D) \[35\sqrt{6}cm\]
E) \[\frac{35\sqrt{2}}{2}cm\]
Correct Answer: A
Solution :
In \[\Delta BCD.\] \[\tan 15{}^\circ =\frac{BC}{BD}\] \[\Rightarrow \] \[\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}=\frac{x}{x+35}\] \[\Rightarrow \] \[\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{x}{x+35}\] \[\Rightarrow \] \[\sqrt{3}x+35\sqrt{3}-x-35=\sqrt{3}x+x\] \[\Rightarrow \] \[2x=35(\sqrt{3}-1)\] \[\Rightarrow \] \[x=\frac{35(\sqrt{3}-1)}{2}\] \[\therefore \]\[CD=\frac{35}{2}\sqrt{{{\left( \frac{\sqrt{3}+1}{2} \right)}^{2}}+{{\left( \frac{\sqrt{3}-1}{2} \right)}^{2}}}\] \[=\frac{35}{2}\times 2\sqrt{2}=35\sqrt{2}\,cm\]You need to login to perform this action.
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