Question
The centroid of an equilateral triangle PQR is L. If PQ
= 18 cm, the length of PL is:Solution
Given: Equilateral triangle PQR with side PQ = 18 cm Formula Used: Circumradius of Equilateral triangle = side of equilateral triangle/√3 Concept Used: Centroid Divide the median in the ratio 2 : 1 All the centers of the Equilateral triangle lie at the same point. Be it circumcenter, orthocenter, incentre, and centroid. ATQ, we can say that : 
 Since all the centers lie at the same point L, PL is also the circumradius of Equilateral Triangle PQR Using the above formula, PL = PQ/√3 ⇒ PL = 18/√3 ⇒ PL = 6√3 cm. ∴  The length of PL is 6√3 cm.
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