The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 3)

Answer 1

Given:

Equilateral triangle PQR with side PQ = 6 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 centres of the Equilateral triangle lie at the same point. Be it circumcenter, orthocenter, incentre, and centroid.

Calculation:

1 (2)

Since all the centres lie at the same point L, PL is also the circumradius of Equilateral Triangle PQR

Using the above formula,

PL = PQ/√3

⇒ PL = 6/√3

⇒ PL = 2√3 cm.

∴ The length of PL is 2√3 cm.