Question

if two triangles, △ abc and △ def are similar, with ab = 16 cm and bc = 32 cm, find \\( \frac { d e } { e f } \\)

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle ABC\) and \(\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{BC}{EF}\). By cross - multiplying, we can get \(\frac{DE}{EF}=\frac{AB}{BC}\).

Step2: Substitute the given values

Given \(AB = 16\mathrm{cm}\) and \(BC=32\mathrm{cm}\). Then \(\frac{DE}{EF}=\frac{16}{32}\).

Step3: Simplify the fraction

\(\frac{16}{32}=\frac{16\div16}{32\div16}=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)