Question

find qr.
qr =

Explanation:

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

Since \( SR\parallel TP\), we have \(\frac{QR}{QT}=\frac{QP}{QP + PT}\). Let \(QR = x\), then \(QT=x + 27\), \(QP=x\), and \(PT = 27\), \(ST = 49\), \(TP=63\). According to the theorem \(\frac{QR}{ST}=\frac{QP}{QP + PT}\).

Step2: Substitute the values into the proportion

Substitute the values into \(\frac{QR}{ST}=\frac{QP}{QP + PT}\), we get \(\frac{x}{49}=\frac{63}{63 + 27}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \((63 + 27)x=49\times63\), \(90x = 49\times63\), \(x=\frac{49\times63}{90}\), \(x=\frac{49\times7}{10}\), \(x = 34.3\).

Answer:

\(34.3\)