Question

find vw.
vw =

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \(TW\parallel UV\), we have \(\frac{ST}{TU}=\frac{SW}{WV}\). Given \(ST = 12\), \(TU=24\), and \(SW = 23\). Let \(WV=x\). Then \(\frac{12}{24}=\frac{23}{x}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(12x=24\times23\). Then \(x=\frac{24\times23}{12}\). Simplify \(\frac{24}{12}=2\), so \(x = 2\times23\).

Answer:

\(46\)