Question

the areas of two similar octagons are 4 m² and 25 m². what is the scale factor of their side lengths? ?:

Explanation:

Step1: Recall the ratio of areas formula

For similar polygons, if the scale factor of side lengths is \(a:b\), the ratio of their areas is \(a^{2}:b^{2}\). Let the scale factor of side lengths be \(x:y\). Then \(\frac{x^{2}}{y^{2}}=\frac{4}{25}\).

Step2: Solve for the scale factor

Take the square - root of both sides of the equation \(\frac{x^{2}}{y^{2}}=\frac{4}{25}\). We know that \(\sqrt{\frac{x^{2}}{y^{2}}}=\frac{x}{y}\) and \(\sqrt{\frac{4}{25}}=\frac{\sqrt{4}}{\sqrt{25}}\). Since \(\sqrt{4} = 2\) and \(\sqrt{25}=5\), then \(\frac{x}{y}=\frac{2}{5}\).

Answer:

\(2:5\)