Question

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.

Answer 1

Let AD be the median of $\Delta ABC$.
Let G be the centroid of $\Delta ABC$.
Let GD = x unit
$\therefore$ Length of median = 12 + x.
Since, centroid divides median in 2:1 ratio.
$\therefore 12:x=2:1$
$\Rightarrow \frac{12}{x}=\frac{2}{1}\Rightarrow x=6$
Hence, length of the median = 12 + 6 = 18 units.