Question

1. \\( \triangle k l m \sim \triangle t s r \\)

\\( r s= \\)

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle KLM\sim\triangle TSR\), the ratios of corresponding sides are equal. That is \(\frac{RS}{LM}=\frac{TS}{KL}\).

Step2: Substitute the known values

We know \(LM = 88\), \(TS=12\), and \(KL = 66\). Substituting into the proportion \(\frac{RS}{88}=\frac{12}{66}\).

Step3: Solve for \(RS\)

Cross - multiply: \(66\times RS=88\times12\). Then \(RS=\frac{88\times12}{66}\). Simplify \(\frac{88\times12}{66}=\frac{8\times11\times12}{6\times11}=\frac{8\times12}{6}\). Further simplify \(\frac{96}{6} = 16\).

Answer:

\(16\)