Question
In ∆ABC , G is the centroid , AB = 18 cm, BC= 24 cm
and AC = 30 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 182 + 302 = 2{AD 2 + (24/2) 2 } or 324 + 900 = 2{AD 2 + 144} or 1224/2 = AD 2 + 144 or 612 = AD 2 + 144 or AD 2 = 612 – 144 = 468 or AD = 6√13 = 6√13 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 6√13 = 6√13/3cm
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