Question

if vw = 18, find zw.

Explanation:

Step1: Recall the centroid theorem

The centroid of a triangle divides each median in a ratio of \(2:1\). Here, \(Z\) is the centroid of \(\triangle TUV\) and \(VW\) is a median. Let \(ZW = x\), then \(ZV=2x\).

Step2: Use the relationship \(VW = ZV + ZW\)

Since \(VW = 18\) and \(VW=ZV + ZW\), and \(ZV = 2ZW\), we substitute \(ZV\) with \(2ZW\). So, \(18=2ZW+ZW\).

Step3: Solve the equation

Combine like - terms: \(18 = 3ZW\). Then, divide both sides by 3: \(ZW=\frac{18}{3}\).

Answer:

\(6\)