Question

in \\( \triangle f g h \\), \\( l \\) is the centroid. if \\( g k = 12 \\), find \\( g l \\).

Explanation:

Step1: Recall the centroid property

The centroid of a triangle divides each median into a ratio of \(2:1\). That is, if \(L\) is the centroid and \(GK\) is a median, then \(GL=\frac{2}{3}GK\).

Step2: Substitute the value of \(GK\)

Given \(GK = 12\), substitute into the formula \(GL=\frac{2}{3}GK\). So \(GL=\frac{2}{3}\times12\).
Calculate \(\frac{2}{3}\times12 = 8\).

Answer:

\(8\)