Question
In ∆ABC , G is the centroid , AB = 8 cm, BC= 12 cm and
AC = 14 cm , find GD, where D is the mid-point of BC?Solution
If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 82 + 142 = 2{AD 2 + (12/2) 2 } or 64 + 196 = 2{AD 2 + 36} or 260/2 = AD 2 + 36 or 130 = AD 2 + 36 or AD 2 = 130 – 36 = 94 or AD = √94 = √94 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of √94 = √94/3cm
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