Question

in \\( \triangle def \\), c is the centroid
if \\( cm = 5 \\), find dc and dm

\\( dc = \square \\) units

Explanation:

Step1: Recall the centroid property

The centroid of a triangle divides each median in a ratio of \(2:1\). That is, if \(C\) is the centroid and \(DM\) is a median (\(M\) is the mid - point of \(EF\)), then \(DC:CM = 2:1\).

Step2: Find \(DC\)

Given \(CM = 5\). Let \(DC=x\). Using the ratio \(DC:CM=2:1\), we have \(\frac{DC}{CM}=\frac{2}{1}\). Substituting \(CM = 5\) into the equation, we get \(x = 2\times5\).

Step3: Find \(DM\)

Since \(DM=DC + CM\), and \(DC = 10\), \(CM = 5\), then \(DM=10 + 5\).

Answer:

\(DC = 10\) units, \(DM=15\) units