Question

If the equation of base of an equilateral triangle is $2x-y=1$ and the vertex is$(-1,2),$ then the length of the sides of the triangle is

• A. $\sqrt{\frac{20}{3}}$
• B. $\frac{20}{3}$
• C. $\sqrt{\frac{8}{15}}$
• D. $\sqrt{\frac{15}{2}}$

Answer 1

The correct option is A $\sqrt{\frac{20}{3}}$

Let the equilateral triangle be ABC and foot of perpendicular from A to BC is AD, then
$AD=|\frac{2(-1)-2-1}{\sqrt{2^2+1^2}}|$ $=\sqrt{5}$
now AB $=cosec{60}^o\times AD=\frac{2}{\sqrt{3}}\times \sqrt{5}=\frac{\sqrt{2}0}{\sqrt{3}}$