Finding the ratios of the perimeters octagons given the ratios of the areas

[Taylor872]

If the area of one regular octagon is 2.5 times that of another, what is the ratio of the perimeters?

i honestly don’t even know where to start with this problem. i just don’t understand ratios at all please help!

 

[MarkFL]

The area of a plane figure will be proportional to the square of a linear measure (such as a perimeter). If two plane figures are similar, then the constant of proportionality will be the same.

So, let's let the area of the larger octagon be:

[MATH]A_L=kP_L^2[/MATH]
And for the smaller octagon:

[MATH]A_S=kP_S^2[/MATH]
Now, we are told:

[MATH]A_L=\frac{5}{2}A_S[/MATH]
or:

[MATH]\frac{A_L}{A_S}=\frac{5}{2}[/MATH]
What do you get when you substitute in for the two areas, using the formulas above?

 

[MarkFL]

To follow up:

[MATH]\frac{kP_L^2}{kP_S^2}=\frac{5}{2}[/MATH]
[MATH]\left(\frac{P_L}{P_S}\right)^2=\frac{5}{2}[/MATH]
[MATH]\frac{P_L}{P_S}=\sqrt{\frac{5}{2}}[/MATH]