Question

1. $qc = 6$. find $ql$.

Explanation:

Step1: Recall the centroid property

The centroid of a triangle divides each median in a ratio of \(2:1\). Here, \(Q\) is the centroid, \(BL\) is a median, and \(QC\) is part of the median - related segments.

Step2: Use the centroid - median ratio formula

If \(Q\) is the centroid of \(\triangle ABC\) and \(BL\) is a median, then \(QC=\frac{2}{3}QL\). Given \(QC = 6\), we can solve for \(QL\) using the formula \(QL=\frac{3}{2}QC\).
Substitute \(QC = 6\) into the formula: \(QL=\frac{3}{2}\times6\).

Step3: Calculate the value of \(QL\)

\(QL=\frac{3\times6}{2}=9\).

Answer:

\(9\)