The centroid of an equilateral triangle ABC is G. If AB

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The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is

1. √3cm
2. 2√3 cm
3. 3√2 cm
4. 2√2cm

Correct Option: B

We draw a figure of an equilateral triangle ABC whose G is centroid and side is 6 cm ,

AB = 6 cm.; AD ⊥ BC
∴ BD = DC = 3 cm.
In ∆ABD,
AD = √AB² – BD²
AD = √6² – 3²
AD = √36 - 9
AD = √27 = 3 √3 cm.

∴ AG =	2	AD =	2	× 3√3
	3		3

AG = 2√3 cm.