Question

△abc ~ △def find the scale factor from △abc to △def.

Explanation:

Step1: Recall the scale - factor formula

The scale factor from \(\triangle ABC\) to \(\triangle DEF\) is \(\frac{\text{side of }\triangle DEF}{\text{side of }\triangle ABC}\) for corresponding sides.

Step2: Identify corresponding sides

Corresponding sides: \(AB = 54\) in \(\triangle ABC\) and \(DE=48\) in \(\triangle DEF\)

Step3: Calculate the scale factor

Scale factor \(k=\frac{DE}{AB}=\frac{48}{54}=\frac{8}{9}\)

Answer:

\(\frac{8}{9}\)