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: Calculate 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 if we consider the ratio of \(OB\) to \(OB'\) in terms of the non - overlapping part (assuming the dilation center is \(O\)), the scale factor \(k=\frac{OB'}{OB}=\frac{5 + 15}{5}=\frac{20}{5} = 4\).

Step2: Use the property of perimeter and dilation

For a dilation, if the scale factor is \(k\), and the perimeter of the original figure is \(P\), the perimeter of the dilated figure \(P'\) is given by \(P'=k\times P\).
Given \(P = 13\) cm and \(k = 4\), then \(P'=4\times13\).

$$P'=52$$

Answer:

\(52\) cm