Question

in △nop, t is the intersection of the three medians. if ot = 30, find ts.

Explanation:

Step1: Recall the centroid property

In a triangle, the centroid (the intersection of the medians) divides each median into a ratio of \(2:1\), where the segment from the vertex to the centroid is twice as long as the segment from the centroid to the midpoint of the opposite side. So, if \(T\) is the centroid, then \(OT = 2 \times TS\).

Step2: Solve for \(TS\)

Given \(OT = 30\), we use the relationship \(OT = 2 \times TS\). Rearranging for \(TS\), we get \(TS=\frac{OT}{2}\). Substituting \(OT = 30\) into the formula, we have \(TS=\frac{30}{2}=15\).

Answer:

15