The centroid of an equilateral triangle ABC is O. If AB = 27 cm, then the length of AO is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 9 cm
Centroid divides the perpendicular of an equilateral triangle in the ratio of 2:1
Height of triangle = (√3/2)× side
⇒(√3/2) × 27
⇒ (27√3)/2
The length of AO will be
⇒ AO = 2/3 of perpendicular × (Height of triangle)
⇒ 2/3 of (27√3/2)
⇒ 9√3 cm