Question

p is the centroid of △lmn. find pn and qp. qn = 21

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median into a ratio of \(2:1\). That is, if \(P\) is the centroid and \(QN\) is a median, then \(QP:PN = 1:2\) and \(QN=QP + PN\). Let \(QP=x\) and \(PN = 2x\). Since \(QN=21\), we have \(x + 2x=21\).

Step2: Solve for \(x\) (QP)

Combine like - terms: \(3x=21\). Divide both sides by 3: \(x=\frac{21}{3}=7\). So \(QP = 7\).

Step3: Solve for \(PN\)

Since \(PN = 2x\) and \(x = 7\), then \(PN=2\times7 = 14\).

Answer:

\(PN = 14\), \(QP = 7\)