Question

use \\( \triangle a b c \\), shown to the right, to answer the following question. if \\( b k = 29 \\), what is \\( k q \\)?

Explanation:

Step1: Recall the centroid property

The centroid of a triangle divides each median in a ratio of \(2:1\). Here, \(K\) is the centroid of \(\triangle ABC\), and \(BP\) is a median. So, \(BK: KQ=2:1\).

Step2: Set up the equation

Let \(KQ = x\). Then \(BK = 2x\). Given \(BK = 29\), we have \(2x=29\).

Step3: Solve for \(x\)

\(x=\frac{29}{2}=14.5\)

Answer:

\(14.5\)