Question

△abc and △def are similar. the missing side length. (the triangles are not drawn to scale.)

Explanation:

Step1: Find the scale factor

Since the triangles are similar, the ratio of corresponding sides is equal. The ratio of side \(AB = 9\) to \(DE=3\) is \(\frac{9}{3}=3\).

Step2: Calculate the missing side

Let the missing side \(DF\) be \(x\). We know that \(\frac{AC}{DF}=\frac{9}{3}\). Given \(AC = 12\), then \(x=\frac{12}{3}\).

Answer:

\(4\)