question_answer

The base of an equilateral triangle is along the line given by \[3x+4y=9\]. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is

A)  \[\frac{2\sqrt{3}}{5}\]                                      

B)  \[\frac{4\sqrt{3}}{5}\]

C)  \[\frac{2\sqrt{3}}{15}\]                                    

D)  \[\frac{4\sqrt{3}}{15}\]

Correct Answer: D

Solution :

As \[h=\frac{\sqrt{3}}{2}\,a\Rightarrow \,\,\frac{2}{5}\,=\frac{\sqrt{3}}{2}\,a\] \[\Rightarrow \,a=\frac{4}{15}\,\sqrt{3}\]