The centroid of an equilateral triangle ΔPQR is L. PQ = 18 cm, then the length if PL is :

$6\sqrt{3}$ cm

We know that,

Centroid Divide the median in the ratio 2 : 1

We have,

PQ = 18 cm

Circumradius of Equilateral triangle = side of equilateral triangle/ \(\sqrt {3}\)

So,PL = PQ/\(\sqrt {3}\)

= PL = 18/\(\sqrt {3}\)

= PL = 6\(\sqrt {3}\) cm.