question_answer

The vertex of an equilateral triangle is (2,-1) and the equation of its base in\[x+2y=1\]. The length of its sides is    [UPSEAT 2003]

A)            \[4/\sqrt{15}\]

B)            \[2/\sqrt{15}\]

C)            \[4/3\sqrt{3}\]                          

D)            \[1/\sqrt{5}\]

Correct Answer: B

Solution :

           \[|AD|\,=\left| \frac{2-2-1}{\sqrt{{{1}^{2}}+{{2}^{2}}}} \right|=\frac{1}{\sqrt{5}}\]              \[\tan 60{}^\circ =\frac{AD}{BD}\]            Þ \[\sqrt{3}=\frac{1\,/\sqrt{5}}{BD}\]            Þ \[BD=\frac{1}{\sqrt{15}}\]            \[BC=2BD=2\,/\sqrt{15}\].