One vertex of an equilateral triangle is `(2,2)` and its centroid is `(-2/sqrt3,2/sqrt3)` then length of its side is

Options

A. `4sqrt(2)`
B. `4sqrt(3)`
C. `3sqrt(2)`
D. `5sqrt(2)`

Answer

A

Explanation

Given are centroid `G(-(2)/(sqrt3),(2)/(sqrt3))` and one vertex `A(2,2)`
`therefore` Length of side of triangle
`=sqrt(3)GA`
`=sqrt(3)sqrt((-(2)/(sqrt3)-2)^2+((2)/(sqrt3)-2)^2)`
`=2sqrt((1+sqrt3)^2+(1-sqrt3)^2)=2sqrt8=4sqrt2`