Question

triangle def is a scaled copy of triangle abc. what is the length of \overline{de}?

Explanation:

Step1: Find the scale factor

Since \( \triangle DEF\) is a scaled - copy of \( \triangle ABC\), we can find the scale factor using the corresponding sides \(BC = 32\) and \(EF=24\). The scale factor \(k\) is given by \(k=\frac{EF}{BC}=\frac{24}{32}=\frac{3}{4}\).

Step2: Calculate the length of \(DE\)

The side \(AB = 36\) in \( \triangle ABC\) corresponds to \(DE\) in \( \triangle DEF\). Using the scale factor \(k=\frac{3}{4}\), we have \(DE=k\times AB\). Substitute \(AB = 36\) and \(k=\frac{3}{4}\) into the formula: \(DE=\frac{3}{4}\times36 = 27\).

Answer:

\(27\)