Question

question
in △bcd, h is the intersection of the three medians. if ch = 28, find cg.

Explanation:

Step1: Recall centroid property

The centroid (intersection of medians) divides each median in a 2:1 ratio. Here, $CH:HG = 2:1$ and $CG=CH + HG$.

Step2: Find $HG$

Since $CH = 28$ and $CH:HG=2:1$, we have $HG=\frac{1}{2}CH$. So $HG=\frac{1}{2}\times28 = 14$.

Step3: Calculate $CG$

$CG=CH + HG$. Substituting the values, $CG=28 + 14=42$.

Answer:

$42$