Question

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

Explanation:

Step1: Set up the proportion

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. So, \(\frac{AB}{DE}=\frac{AC}{DF}\).
Given \(AB = 3\), \(DE=2\), \(AC = 7\), and let \(DF=x\). Then the proportion is \(\frac{3}{2}=\frac{7}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(3x=2\times7\).

Step3: Solve for \(x\)

\(3x = 14\), so \(x=\frac{14}{3}\).

Answer:

\(\frac{14}{3}\)