Question

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

1. 9√3 cm
2. 6√3 cm
3. 7√3 cm
4. 8√3 cm

Answer 1

Correct Answer - Option 1 : 9√3 cm

Given :

The centroid of a triangle ABC is O

The length of the side of the triangle is 27 cm

Concept used :

Centroid divides the upper part & lower part of the perpendicular inside an equilateral triangle in 2 : 1

Height of triangle = (√3/2)× side

Calculations :

Height of triangle = (√3/2) × 27

⇒ (27√3)/2

Now the length of AO 

⇒ AO = 2/3 of perpendicular × (Height)

⇒ 2/3 of (27√3/2)

⇒ 9√3 cm

∴ The correct choice will be option 1.