Question

triangle abc is similar to triangle def. solve for r. r =

Explanation:

Step1: Set up proportion

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. So, \(\frac{AC}{DE}=\frac{BC}{EF}\). Substituting the values: \(\frac{12}{18}=\frac{6}{r}\).

Step2: Cross - multiply

Cross - multiplying gives \(12r = 18\times6\).

Step3: Solve for \(r\)

First, calculate \(18\times6 = 108\). Then, \(r=\frac{108}{12}\).

Answer:

\(9\)