Question

in \\( \triangle def \\), \\( c \\) is the centroid
if \\( dm = 27 \\), find \\( dc \\) and \\( cm \\)
\\( dc = 18 \\) units
\\( cm = \square \\) units

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 and \(DM\) is a median, then \(DC=\frac{2}{3}DM\) and \(CM = \frac{1}{3}DM\).

Step2: Calculate \(CM\)

Given \(DM = 27\). Using the formula \(CM=\frac{1}{3}DM\), substitute \(DM = 27\) into the formula.

$$CM=\frac{1}{3}\times27$$

$$CM = 9$$

Answer:

\(CM = 9\) units