Question

triangle abc and def are similar. what is the length of \\(\overline{ef}\\)?
(image of two triangles: triangle abc with sides bc=3 cm, ac=4 cm, ab=6 cm; triangle def with side df=4 cm, ed=12 cm, and ef unknown)

Explanation:

Step1: Identify Similar Triangles Ratio

Since \(\triangle ABC \sim \triangle DEF\), corresponding sides are proportional. In \(\triangle ABC\), \(AB = 6\) cm, \(AC = 4\) cm, \(BC = 3\) cm. In \(\triangle DEF\), \(DE = 12\) cm, \(DF = 4\) cm, and \(EF\) is unknown. The ratio of \(DE\) to \(AB\) is \(\frac{12}{6}=2\).

Step2: Apply Proportionality to \(EF\)

The side \(BC\) in \(\triangle ABC\) corresponds to \(EF\) in \(\triangle DEF\). So, \(EF = BC\times\) ratio. \(BC = 3\) cm, ratio \(= 2\), so \(EF = 3\times2 = 6\) cm.

Answer:

\(6\) cm