Question

pt || qs. find st.

Explanation:

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

Since \(PQ\parallel TS\), we have \(\frac{PQ}{TS}=\frac{PR}{TR}\). Let \(TS = x\). Here, \(PQ = 30\), \(PR=60 + 24=84\), and \(TR = 60\).

Step2: Set up the proportion equation

\(\frac{30}{x}=\frac{60}{84}\). Cross - multiply to get \(60x=30\times84\).

Step3: Solve for \(x\)

\(x=\frac{30\times84}{60}\). Simplify \(\frac{30\times84}{60}=\frac{84}{2}=42\).

Answer:

\(42\)