Question

triangles abc and def are similar triangles. diagram of triangles abc (a, b, c with ab = 5 in, bc = 6 in) and def (d, e, f with ef = 13 in) use this fact to solve the exercise. round to the nearest tenth. find side de (in inches).

Explanation:

Step1: Identify corresponding sides

Since triangles \(ABC\) and \(DEF\) are similar, corresponding sides are proportional. In \(\triangle ABC\), \(AB = 5\) in, \(BC = 6\) in. In \(\triangle DEF\), \(EF = 13\) in, and we need to find \(DE\). The corresponding sides are \(AB\) and \(DE\), \(BC\) and \(EF\). So the proportion is \(\frac{AB}{DE}=\frac{BC}{EF}\).

Step2: Substitute values into proportion

Substitute \(AB = 5\), \(BC = 6\), \(EF = 13\) into the proportion: \(\frac{5}{DE}=\frac{6}{13}\).

Step3: Solve for \(DE\)

Cross - multiply: \(6\times DE=5\times13\). So \(6DE = 65\). Then \(DE=\frac{65}{6}\approx10.8\) (rounded to the nearest tenth).

Answer:

\(10.8\)