Q. 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
A) $\sqrt{\frac{20}{3}}$
B) $\frac{2}{\sqrt{15}}$
C) $\sqrt{\frac{8}{15}}$
D) $\sqrt{\frac{15}{2}}$
Explanation
(a)
$\because AD = \left| \frac{- 2 - 2 - 1}{\sqrt{(2)^{2} + ( - 1)^{2}}} \right| = \left| \frac{- 5}{\sqrt{5}} \right| = \sqrt{5}$
$and\ in\ \mathrm{\Delta}\ ABD\ \tan{60{^\circ}} = \frac{AD}{BD}$
[image:10_image32.emf]
$\Rightarrow \sqrt{3} = \frac{\sqrt{5}}{BD}\ \Rightarrow \ BD = \sqrt{\frac{5}{3}}$
$\therefore\ BC = 2BD = 2\sqrt{\frac{5}{3}} = \sqrt{\frac{20}{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.