Question

if ( bh = 24 ), find ( bf ).

Explanation:

Step1: Recall the centroid property

In a triangle, the centroid divides each median in a ratio of \(2:1\). Here, \(H\) is the centroid of \(\triangle BCD\) and \(BF\) is a median.

Step2: Set up the relationship

Let \(BH = 2x\) and \(HF=x\). Given \(BH = 24\), so \(2x = 24\), then \(x=\frac{24}{2}=12\).

Step3: Calculate \(BF\)

Since \(BF=BH + HF\), and \(BH = 24\), \(HF = 12\), then \(BF=24 + 12=36\).

Answer:

\(BF = 36\)