Question

rs || qt. find qr. qr = submit work it out

Explanation:

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

Since \( \overline{RS}\parallel\overline{QT}\), we have \(\frac{PQ}{QR}=\frac{PT}{TS}\). Let \(QR = x\). Then \(PQ=18\), \(PT = 38\), \(TS = 57\). The proportion becomes \(\frac{18}{x}=\frac{38}{57}\).

Step2: Cross - multiply

Cross - multiplying gives \(38x=18\times57\).

Step3: Solve for \(x\)

First, calculate \(18\times57 = 1026\). Then \(x=\frac{1026}{38}=27\).

Answer:

\(27\)