The ratio of areas of two regular polygons with same number of sides is 4:9. What is the ratio of their side lengths?
2:3
For regular polygons with the same number of sides, the ratio of their areas equals the square of the ratio of their side lengths, so \(\frac{A_1}{A_2} = \left(\frac{s_1}{s_2}\right)^2\).
Given \(\frac{A_1}{A_2} = \frac{4}{9}\), we get \(\left(\frac{s_1}{s_2}\right)^2 = \frac{4}{9}\).
Taking the square root of both sides, \(\frac{s_1}{s_2} = \frac{2}{3}\).
Hence, the answer is 2:3.
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