The areas of two similar figures are 20 cm2 and 45 cm2. What is the scale factor of their corresponding sides? What is the ratio of their perimeters?
The solution to the answer is as follows:
sqrt(20/45)
= sqrt(4/9)
= 2/3 (scalar factor of sides, ratio perimeters)
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The scale factor of their corresponding sides is, \(\frac{2}{3}\)
The ratio of their perimeters is \(\frac{2}{3}\)
When two triangles are similar. Then the relation between their area and corresponding sides are shown below;
\(\frac{Area_{1}}{Area_{2}} =\sqrt{\frac{side_{1}}{side_{2}}}\)
It is given that, the areas of two similar figures are \(20 cm^{2}\) and \(45 cm^{2}\).
Therefore, the scale factor of their corresponding sides is,
\(=\sqrt{\frac{20}{45}} =\sqrt{\frac{4}{9} } = \frac{2}{3}\)
the ratio of their perimeters is \(\frac{2}{3}\)
Learn more about the similar triangle here:
https://brainly.com/question/14285697