Question

p≠454. if △pqr ~ △vst with a scale factor of 2:5, find the value of x.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle PQR\sim\triangle VST\), the ratio of corresponding sides is equal to the scale factor. The scale factor is \(2:5\), which means \(\frac{QR}{ST}=\frac{2}{5}\).

Step2: Substitute the known values

We know that \(ST = 30\). Let \(QR=x\). Then \(\frac{x}{30}=\frac{2}{5}\).

Step3: Solve for \(x\)

Cross - multiply: \(5x=2\times30\). So \(5x = 60\), and \(x=\frac{60}{5}=12\).

Answer:

\(12\)