Question

Find the scale factor and ratio of perimeters forpair of similar octagons with areas 25 ft?and81 ft?.1. The scale factor iS(Simplify your answer.)2. The ratio of perimeters IS(Simplify your answer.)

Answer 1

ANSWERS

1. 5/9

2. 5/9

Step-by-step explanation

1. The ratio of the areas between similar polygons is the square of the scale factor. In this case, the areas of the polygons are 25 ft² and 81 ft², so the ratio between their areas is,

`(25)/(81)`

The scale factor is the square root of this ratio,

`\sqrt{(25)/(81)}=(√(25))/(√(81))=(5)/(9)`

Hence, the scale factor is 5/9.

2. The ratio of perimeters is equal to the scale factor when it is simplified. Hence the ratio of perimeters is 5/9.