2 Squares and their ratios. I just found this out.
The ratio of the areas of the squares, and the ratio of their perimeter. It looks like they're connected in some way.
As an example:
if you have a square 20X20 and another one with 100X100
The the ratio of the areas is 1:25, and the ratio of the perimeters is 1:5.
These are the same if you multiply ratio of perimeter with 5.
Another example:
12.75X12.75 and a 50.35X50.35.
The ratio of the areas is about: 162.5625:2535.1225
The ratio of the perimeters is about: 51:201.4
These can be made to these | 1:15.5947 | 1:3.9490 | 
These are also the same if you multiply ratio of perimeter with 4, if you had the rest of the decimal numbers.
Does this apply with all ratios or is this just a coincidence?

It is quite general and comes from the dimesionality of area and perimeter.  If you scale any figure up by a factor $k$ the area increases by a factor $k^2$ and the perimeter increases by a factor $k$.  The ratio area/perimeter then increases by a factor $k$ as well.  
In three dimensions on scaling a figure by $k$ the volume scales as $k^3$ and the surface area by $k^2$
