Question

1. \\( \triangle u v w \sim \triangle u s t \\)

Explanation:

Step1: Identify similar triangles ratio

Since \(\triangle UVW \sim \triangle UST\), the ratios of corresponding sides are equal. The sides \(UW = 12\), \(UT = 6\), and \(UV = 26\), let \(US = x\) (the unknown side). The ratio of \(UW\) to \(UT\) is \(\frac{12}{6}=2\), so the ratio of \(UV\) to \(US\) should also be 2.

Step2: Set up proportion

\(\frac{UV}{US}=\frac{UW}{UT}\) becomes \(\frac{26}{x}=\frac{12}{6}\). Simplify \(\frac{12}{6}=2\), so \(\frac{26}{x}=2\).

Step3: Solve for \(x\)

Multiply both sides by \(x\): \(26 = 2x\). Divide by 2: \(x=\frac{26}{2}=13\).

Answer:

13