Question

each figure shows a triangle with one or more of its medians.

1. find ub if br = 17

Explanation:

Step1: Recall the property of the centroid of a triangle

The centroid of a triangle divides each median into a ratio of \(2:1\). That is, if \(B\) is the centroid of \(\triangle TUV\) and \(BR\) is a part of the median \(VR\), then \(BR=\frac{2}{3}VR\) and \(UB=\frac{1}{3}VR\). Also, we know that \(BR + UB=VR\).

Step2: Use the ratio relationship

Since \(BR:UB = 2:1\), let \(UB=x\). Then \(BR = 2x\). Given \(BR = 17\), we have the equation \(2x=17\). Solving for \(x\), we get \(x=\frac{17}{2}=8.5\)

Answer:

\(8.5\)