Question

in \\( \triangle b c d \\), \\( h \\) is the intersection of the three medians. if \\( c h = 28 \\), find \\( c g \\).

Explanation:

Step1: Recall the property of the centroid of a triangle

The centroid \(H\) of a triangle divides each median in a ratio of \(2:1\). That is, if \(H\) is the centroid and \(CG\) is a median with \(H\) on \(CG\), then \(CH=\frac{2}{3}CG\).

Step2: Solve for \(CG\)

Given \(CH = 28\) and \(CH=\frac{2}{3}CG\). We can rewrite the formula to solve for \(CG\) as \(CG=\frac{3}{2}CH\).
Substitute \(CH = 28\) into the formula: \(CG=\frac{3}{2}\times28\).
Calculate \(\frac{3}{2}\times28=3\times14 = 42\).

Answer:

\(42\)