Question

the areas of two similar octagons are 9 m² and 25 m². what is the scale factor of their side lengths? 3:?

Explanation:

Step1: Recall the relationship between areas and side - lengths of similar polygons

For two similar polygons, if the scale factor of their side - lengths is \(k\), the ratio of their areas is \(k^{2}\). Let the scale factor of the side - lengths of the two similar octagons be \(a:b\), then the ratio of their areas is \(a^{2}:b^{2}\).

Step2: Set up the ratio of the areas

We know that the areas of the two similar octagons are \(9m^{2}\) and \(25m^{2}\), so \(\frac{a^{2}}{b^{2}}=\frac{9}{25}\).

Step3: Solve for the ratio of the side - lengths

Taking the square root of both sides of the equation \(\frac{a^{2}}{b^{2}}=\frac{9}{25}\), we get \(\frac{a}{b}=\sqrt{\frac{9}{25}}=\frac{3}{5}\).

Answer:

5