Question

find pt.
pt =

Explanation:

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

Since \(QT\parallel SR\), we have \(\frac{PT}{TS}=\frac{PQ}{QR}\). Given \(PQ = 40\), \(QR=60\), and \(TS = 9\). Let \(PT=x\). Then \(\frac{x}{9}=\frac{40}{60}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(60x=40\times9\). So \(60x = 360\). Divide both sides by 60: \(x=\frac{360}{60}\).

Answer:

\(6\)