question_answer

If the equation of base of an equilateral triangle is \[2x-y=1\] and the vertex is (?1, 2), then the length of the side of the triangle is [Kerala (Engg.) 2005]

A)            \[\sqrt{\frac{20}{3}}\]              

B)            \[\frac{2}{\sqrt{15}}\]

C)            \[\sqrt{\frac{8}{15}}\]              

D)            \[\sqrt{\frac{15}{2}}\]

Correct Answer: A

Solution :

           \[AD=\left| \,\frac{-2-2-1}{\sqrt{{{(2)}^{2}}+{{(-1)}^{2}}}}\, \right|=\left| \,\frac{-5}{\sqrt{5}}\, \right|=\sqrt{5}\]                    \[\because \] \[\tan {{60}^{o}}\] \[=\frac{AD}{BD}\Rightarrow \sqrt{3}=\frac{\sqrt{5}}{BD}\]Þ \[BD=\sqrt{\frac{5}{3}}\]                                 \[\therefore \] \[BC=2BD=2\sqrt{\frac{5}{3}}=\sqrt{\frac{20}{3}}\].