The centroid of a triangle is located 12 units from one of the vertices of a triangle. Find the length of the median of the triangle drawn from that same vertex.
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Solution
Let AD be the median of ΔABC.
Let G be the centroid of ΔABC.
Let GD = x unit ∴ Length of median = 12 + x.
Since, centroid divides median in 2:1 ratio. ∴12:x=2:1 ⇒12x=21⇒x=6
Hence, length of the median = 12 + 6 = 18 units.