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      Question

      In ∆ABC , G is the centroid , AB = 12 cm, BC= 16 cm

      and AC = 20 cm , find GD, where D is the mid-point of BC?
      A 2√86/3 cm Correct Answer Incorrect Answer
      B 2√7/3 cm Correct Answer Incorrect Answer
      C 8√7/3 cm Correct Answer Incorrect Answer
      D 4√13/3 cm Correct Answer Incorrect Answer

      Solution

      If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 122 +  202  = 2{AD 2 + (16/2) 2 } or 144 + 400 = 2{AD 2 + 64} or 544/2 =  AD 2  + 64 or 272 = AD 2  + 64 or  AD 2  = 272 – 64 = 208  or AD = √208 = 4√13 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 4√13 = 4√13/3cm

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