Question

triangles abc and def are similar.
type your answers in the boxes.
a. find the length of segment bc.
units

Explanation:

Step1: Find the scale factor

Since the triangles are similar, the ratio of corresponding sides is equal. The ratio of side \(AB = 3\) to \(DE=2\) is the scale factor. The scale factor \(k=\frac{AB}{DE}=\frac{3}{2}\)

Step2: Relate the sides \(BC\) and \(EF\)

We know that \(\frac{BC}{EF}=\frac{AB}{DE}\). Given \(EF = \frac{12}{5}\), let \(BC=x\). Then \(\frac{x}{\frac{12}{5}}=\frac{3}{2}\)

Cross - multiply: \(2x=\frac{12}{5}\times3\)

\(2x=\frac{36}{5}\)

Solve for \(x\): \(x=\frac{36}{5}\div2=\frac{36}{5}\times\frac{1}{2}=\frac{18}{5} = 3.6\)

Answer:

\(3.6\)