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    Question

    The centroid of an equilateral triangle PQR is L. If PQ

    = 18 cm, the length of PL is:
    A 4√3 cm Correct Answer Incorrect Answer
    B 3√3 cm Correct Answer Incorrect Answer
    C 6√3 cm Correct Answer Incorrect Answer
    D 5√3 cm Correct Answer Incorrect Answer

    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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