Question

in △tuv, y is the centroid. if tw = 30, what is vw? 5 10 60 15

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a ratio of 2:1. That is, if \(YW\) is part of a median and \(TW\) is the whole - length of the median from vertex \(T\) to the mid - point of the opposite side, and \(Y\) is the centroid, then \(TY:YW = 2:1\) and \(TW=TY + YW\).
Let \(YW=x\), then \(TY = 2x\), and \(TW=3x\).

Step2: Solve for \(x\)

Given \(TW = 30\). Since \(TW=3x\), we have the equation \(3x=30\).
Dividing both sides of the equation by 3, we get \(x=\frac{30}{3}=10\).

Answer:

10