Question

The areas of two similar octagons are 4m^(2) and 25m^(2). What is the scale factor of their side lengths?

Answer 1

The scale factor of the side lengths of the two similar octagons is 2.5.

Step-by-step explanation:

The scale factor of the side lengths of two similar octagons can be found by taking the square root of the ratio of their areas. In this case, the area of the first octagon is 4m2 and the area of the second octagon is 25m2. So the ratio of their areas is 25/4. Taking the square root of this ratio gives us the scale factor of the side lengths:

Square root of 25/4 = 5/2 = 2.5

Therefore, the scale factor of the side lengths of the two similar octagons is 2.5.

Answer 2

The scale factor of the side lengths is 2/5.

Step-by-step explanation:

The scale factor is determined by comparing the areas of the two similar octagons.

The ratio of their areas is equal to the square of the scale factor. In this case, the ratio of the areas is 4m2/25m2.

Simplifying this ratio, we get 1/6.25.

To find the scale factor, we take the square root of the ratio.

Therefore, the scale factor of their side lengths is 1/2.5 or 2/5.

This means the side length of the smaller octagon is multiplied by 2/5 to get the side length of the larger octagon.