Question

in \\( \triangle def \\), \\( c \\) is the centroid
if \\( dm = 27 \\), find \\( dc \\) and \\( cm \\)
\\( dc = \square \\)

Explanation:

Step1: Recall the centroid property

The centroid of a triangle divides each median into a ratio of \(2:1\). That is, if \(C\) is the centroid of \(\triangle DEF\) and \(DM\) is a median, then \(DC=\frac{2}{3}DM\) and \(CM = \frac{1}{3}DM\).

Step2: Calculate \(DC\)

Given \(DM = 27\). Using the formula \(DC=\frac{2}{3}DM\), we substitute \(DM = 27\) into the formula:
\(DC=\frac{2}{3}\times27\)
\(DC = 18\)

Answer:

\(DC = 18\)