Question

triangles abc and def are similar. find the length of segment bc

Explanation:

Step1: Set up the proportion

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. So, \(\frac{AB}{DE}=\frac{BC}{EF}\).
Given \(AB = 3\), \(DE=2\), and \(EF=\frac{14}{3}\).

Step2: Solve for \(BC\)

Substitute the values into the proportion \(\frac{3}{2}=\frac{BC}{\frac{14}{3}}\).
Cross - multiply: \(2\times BC=3\times\frac{14}{3}\).
Simplify: \(2BC = 14\).
Divide both sides by 2: \(BC=\frac{14}{2}=7\).

Answer:

\(7\)