Question

pq || rt. find rs.
rs =

Explanation:

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

Since \( \overline{PQ}\parallel\overline{RT}\), we have \(\frac{RS}{RQ}=\frac{ST}{TP}\). Let \(RS = x\), then \(RQ=24\), \(ST = 22\), and \(TP=66\).

Step2: Substitute values into the proportion

\(\frac{x}{24}=\frac{22}{66}\)
Cross - multiply: \(66x=24\times22\)

Step3: Solve for \(x\)

\(x=\frac{24\times22}{66}\)
\(x = 8\)

Answer:

\(8\)