Question

the perimeter of \\( \triangle abc \\) is 13 cm. it was dilated to create \\( \triangle abc \\). what is the perimeter of \\( \triangle abc \\)? 13 cm 26 cm 39 cm 52 cm

Explanation:

Step1: Find the scale factor

The scale factor \(k\) of dilation is calculated by the ratio of corresponding side lengths. Here, \(OB = 5\) and \(OB'=5 + 15=20\). But wait, no, if we consider the dilation from \(\triangle ABC\) to \(\triangle A'B'C'\), looking at the segments from the center of dilation \(O\): \(OB = 5\) and \(OB'=5+15 = 20\). The scale factor \(k=\frac{OB'}{OB}=\frac{20}{5}=4\).

Step2: Use the property of perimeter of similar figures

If two similar figures (a dilated figure and the original figure are similar) have a scale factor \(k\), and the perimeter of the original figure is \(P\) and the perimeter of the dilated figure is \(P'\), then \(P'=k\times P\). Given \(P = 13\) cm and \(k = 4\).

So \(P'=4\times13\)

$$P'=52$$

Answer:

\(52\) cm