Question

    In ∆ABC , G is the centroid , AB = 18 cm, BC= 24 cm

    and AC = 30 cm , find GD, where D is the mid-point of BC?
    A √94/3 cm Correct Answer Incorrect Answer
    B 2√79/3 cm Correct Answer Incorrect Answer
    C √79/3 cm Correct Answer Incorrect Answer
    D 6√13/3 cm Correct Answer Incorrect Answer

    Solution

    If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 182 +  302  = 2{AD 2 + (24/2) 2 } or 324 + 900 = 2{AD 2 + 144} or 1224/2 =  AD 2  + 144  or 612 = AD 2  + 144  or  AD 2  = 612 – 144 = 468 or AD = 6√13 = 6√13 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 6√13 = 6√13/3cm

    Practice Next

    Relevant for Exams:

    ask-question