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    Question

    In ∆ABC , G is the centroid , AB = 5 cm, BC= 8 cm and

    AC = 7 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 √21/3 cm Correct Answer Incorrect Answer

    Solution

    If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 52 +  72  = 2{AD 2 + (8/2) 2 } or 25 + 49 = 2{AD 2 + 16} or 74/2 =  AD 2  + 16  or  37 = AD 2  + 16 or  AD 2  = 37 – 16 = 21  or AD = √21 = √21 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of √21 = √21/3cm

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