Question

in △def, c is the centroid. if dm = 18, find dc and cm dc = □ 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 (\(DM = DC+CM\)), then \(DC=\frac{2}{3}DM\) and \(CM = \frac{1}{3}DM\).

Step2: Calculate \(DC\)

Given \(DM = 18\). Using the formula \(DC=\frac{2}{3}DM\), substitute \(DM = 18\) into the formula:
\(DC=\frac{2}{3}\times18\)
\(DC = 12\)

Step3: Calculate \(CM\) (optional as per the question's direct ask for \(DC\), but shown for completeness)

Using \(CM=\frac{1}{3}DM\), substitute \(DM = 18\)
\(CM=\frac{1}{3}\times18=6\)

Answer:

\(DC = 12\) units