Question

Find the scale factor and ratio of perimeters for a pair of similar octagons with areas 36 ft squared and 49 ft squared.

Answer 1

Answer:

scale factor: 1.16

perimeters: 21.84 ft and 25.36 ft

Step-by-step explanation:

The area for an octagon is as follows:

$A = 2*l^{2}(1+\sqrt{2})$

solved for "l":

$l = \sqrt{\frac{A}{2*(1+\sqrt{2}) } }$

now we calculate the value of each side:

$l1 = \sqrt{\frac{36}{2*(1+\sqrt{2}) } }$

l1 = 2.73

$l2 = \sqrt{\frac{49}{2*(1+\sqrt{2}) } }$

l2 = 3.17

The scale would be:

3.17 / 2.73 = 1.16

And the value of the perimeter of the first would be:

2.73 * 8 = 21.84

and the second:

3.17 * 8 = 25.36