Question

If 2 similar regular hexagons have areas of 25√3 cm² and 16√3 cm² respectively. What is the scale factor from smaller to larger pentagon?​

Answer 1

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

In this case, we have two similar regular hexagons. Let x be the side length of the smaller hexagon, and y be the side length of the larger hexagon. Then, we have:

Area of smaller hexagon / Area of larger hexagon = (x^2 * 6 * sqrt(3)) / (y^2 * 6 * sqrt(3)) = x^2 / y^2

We are given the areas of the two hexagons:

x^2 * 6 * sqrt(3) = 16 * sqrt(3)

y^2 * 6 * sqrt(3) = 25 * sqrt(3)

Dividing the second equation by the first equation, we get:

(y^2 * 6 * sqrt(3)) / (x^2 * 6 * sqrt(3)) = 25 * sqrt(3) / (16 * sqrt(3))

Simplifying this expression gives:

y^2 / x^2 = 25 / 16

Taking the square root of both sides, we get:

y / x = 5 / 4

Therefore, the scale factor from the smaller hexagon to the larger hexagon is 5/4.