If the areas of two similar hexagons are to each other as 5 : 2, and one side of the first hexagon is 25, what is the corresponding side in the other hexagon?

The area of a hexagon is given by (3sqrt(3) / 2) x a^2 where a is the side of the hexagon. Given that the ratio of the area of two similar hexagons is 5 : 2. This means that the ratio of the square of the sides is 5 : 2. Let the corresponding side in the other hexagon be x, then: 25^2 : x^2 = 5 : 2 625 / x^2 = 5 / 2 x^2 = (625 x 2) / 5 = 250 x = sqrt(250) = 15.8 Therefore, the corresponding side in the other hexagon is approximately 15.8

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