Question

if ts = 3, find os.

Explanation:

Step1: Recall the centroid property

The centroid of a triangle divides each median in a ratio of \(2:1\). Here, \(T\) is the centroid of \(\triangle ONP\) and \(OS\) is a median. So, \(OT:TS = 2:1\), and \(OS=OT + TS\).

Step2: Express \(OT\) in terms of \(TS\)

Since \(OT = 2TS\) (from the centroid - median ratio property) and \(TS = 3\).

Step3: Calculate \(OS\)

Substitute \(OT = 2\times3\) into \(OS=OT + TS\). Then \(OS=2TS+TS=3TS\).

Answer:

\(OS = 9\)