Question

as shown below, the medians of \\( \triangle abc \\) intersect at \\( d \\).
if the length of \\( \overline{be} \\) is 12, what is the length of \\( \overline{bd} \\)?

1. 8
2. 9
3. 3
4. 4

Explanation:

Step1: Recall the property of the centroid

The medians of a triangle intersect at the centroid. The centroid divides each median into a ratio of \(2:1\). That is, if \(D\) is the centroid of \(\triangle ABC\) and \(BE\) is a median, then \(BD=\frac{2}{3}BE\) and \(DE = \frac{1}{3}BE\).

Step2: Substitute the value of \(BE\)

Given \(BE = 12\). Using the formula \(BD=\frac{2}{3}BE\), we substitute \(BE\) with \(12\). So \(BD=\frac{2}{3}\times12\).

$$ BD=\frac{2\times12}{3}=8 $$

Answer:

\(8\)