The centroid of an equilateral triangle ΔABC is O. If AB = 27 cm, then the length of  AO is :

$9\sqrt{3}$ cm $6\sqrt{3}$ cm $7\sqrt{3}$ cm $8\sqrt{3}$ cm

$9\sqrt{3}$ cm

AB = 27 cm Height of traingle = \(\frac{2}{√3}\) × Side of triangle = \(\frac{√3}{2}\) × 27 = \(\frac{27√3}{2}\) Now, AO = \(\frac{2}{3}\) × Height of triangle = \(\frac{2}{3}\) ×  \(\frac{27√3}{2}\)  = 9√3 cm