Question

each pair of polygons are similar. find the missing side le

1. \\( \triangle stu \sim \triangle pqr \\)

4.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle STU\sim\triangle PQR\), the ratios of corresponding sides are equal. That is \(\frac{PQ}{ST}=\frac{QR}{TU}=\frac{PR}{SU}\).

Step2: Set up the proportion

We know \(PQ = 4\), \(ST=6\), \(QR = x\), \(TU = 8\). Using the ratio \(\frac{PQ}{ST}=\frac{QR}{TU}\), we get \(\frac{4}{6}=\frac{x}{8}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(6x=4\times8\), so \(6x = 32\), then \(x=\frac{32}{6}=\frac{16}{3}\approx5.33\).

Answer:

\(x = \frac{16}{3}\)