Question

vw || su. find uv.

Explanation:

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

Since \( \overline{VW}\parallel\overline{SU}\), by the basic proportionality theorem in \(\triangle VWT\), we have \(\frac{UV}{UT}=\frac{WS}{ST}\).
Let \(UV = x\), then \(UT = 42\), \(WS = 11\), and \(ST = 22\). So the proportion is \(\frac{x}{42}=\frac{11}{22}\).

Step2: Solve the proportion for \(x\)

Cross - multiply the proportion \(\frac{x}{42}=\frac{11}{22}\). We get \(22x=11\times42\).
Since \(11\times42 = 462\), then \(x=\frac{462}{22}\).
Simplify \(\frac{462}{22}\), \(462\div22 = 21\).

Answer:

\(21\)