Question

in \\( \triangle def \\), \\( c \\) is the centroid.
if \\( dm = 36 \\), find \\( dc \\) and \\( cm \\)
\\( dc = 24 \\) units
\\( cm = \square \\) units

Explanation:

Step1: Recall centroid property

The centroid divides each median into a ratio of \(2:1\). So \(DC:CM = 2:1\) and \(DM=DC + CM\). Let \(CM=x\), then \(DC = 2x\).

Step2: Substitute into \(DM\) equation

Since \(DM=36\), we have \(2x+x=36\), which simplifies to \(3x = 36\).

Step3: Solve for \(x\)

Dividing both sides by \(3\), we get \(x=\frac{36}{3}=12\).

Answer:

\(CM = 12\) units