Question

in \\( \triangle g h i \\), \\( m \\) is the intersection of the three medians. if \\( g m = 24 \\), find \\( g k \\).

Explanation:

Step1: 中线交点性质

三角形三条中线的交点（重心）将每条中线分为\(2:1\)的两段，即\(GM = \frac{2}{3}GK\)。

Step2: 计算\(GK\)

已知\(GM = 24\)，由\(GM = \frac{2}{3}GK\)可得\(GK=\frac{3}{2}GM\)，将\(GM = 24\)代入，\(GK=\frac{3}{2}\times24\)。

Answer:

\(36\)