In ∆ABC , G is the centroid , AB = 5 cm, BC= 6 cm and AC = 7 cm , find GD, where D is the mid-point of BC?
If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 5 2 + 72 = 2{AD 2 + (6/2) 2 } or 25 + 49 = 2{AD 2 + 9} or 74/2 = AD 2 + 9 or 37 = AD 2 + 9 or AD 2 = 37 – 9 = 28 or AD = √28 = 2√7 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 2√7 = 2√7 /3cm
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