Remember: In an equilateral triangle, centroid, orthocentre and circumcentre coincide. So, O is the centroid of the trianglePQR also. Now, O divides PL in the ratio 2:1,i.e.,OP:OL=2:1. ∴OP=
2
3
PL ⇒PL=
3
2
OP=
3
2
×8=12cm PL=
√3
2
PQ ⇒PQ=
2×12
√3
=8√3cm Therefore, perimeter of ΔPQR = 3PQ =3×8√3=24√3cm