A) \[x\sqrt{2}\]
B) \[\frac{x}{\sqrt{2}}\]
C) \[\frac{x}{2\sqrt{2}}\]
D) \[\frac{x}{4}\]
Correct Answer: C
Solution :
Let the height of the shorter and the longer pole be \[h\] and\[2h\], respectively. e In\[\Delta ABM,\] \[\tan \theta =\frac{AB}{BM}=\frac{h}{x/2}=\frac{2h}{x}\] ... (i) In\[\Delta CDM,\] \[\tan ({{90}^{o}}-\theta )=\frac{CD}{MD}\] \[=\frac{2h}{x/2}=\frac{4h}{x}\] \[\Rightarrow \] \[\cot \theta =\frac{4h}{x}\] ... (ii) On multiplying both the equations, we get \[1=\frac{2h}{x}\cdot \frac{4h}{x}\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{8}={{k}^{2}}\] \[\Rightarrow \] \[h=\frac{x}{2\sqrt{2}}\]You need to login to perform this action.
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