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?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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