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One vertex of an equilateral triangle is...

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

A

`4sqrt(2)`

B

`4sqrt(3)`

C

`3sqrt(2)`

D

`5sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
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`
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