Question

One vertex of an equilateral triangle is $(2,2)$ and its centroid is $(\frac{-2}{\sqrt{3}},\frac{2}{\sqrt{3}})$ then length of its side is

• A. $4\sqrt{2}$
• B. $4\sqrt{3}$
• C. $3\sqrt{2}$
• D. $5\sqrt{2}$

Answer 1

The correct option is A $4\sqrt{2}$

The distance between the vertex and centroid of an euilateral triangle gives us the circumradius of the triangle.

$r^2=(x_1-x_2{)}^2+(y_1-y_2{)}^2$

$={(2-\frac{2}{\sqrt{3}})}^2$ +${(2+\frac{2}{\sqrt{3}})}^2$

Circum-radius = $\sqrt{\frac{32}{3}}$

Length of side = $r\sqrt{3}=\sqrt{32}=4\sqrt{2}$