I have a ratio I want to illustrate by geometry. That ratio is $27/25 = (\frac{3\sqrt3}{5})^2$ = 1.08
So I have made this illustration but I can't figure out, how to make a transformation between dimensions. I know that FIHG area is $\frac{3\sqrt3}{5}$ so I would need to square it maybe?
Is it possible by some geometric transformation or other procedure?
Other thing I was thinking if area could be transformed to a length rather than area. So final length would be 1.08 (N) compared to 1.00 (A).
You see, I'm not familiar with this kind of geometric mutations at all so my terminology and approach might seem odd. I hope I can give more information if needed.
I was also thinking if 3 cubed per 5 squared could be illustrated by 3D cube (3*3*3) and splitting plane (5*5) but I had same problem. What is the result in geometric sense when you divide 3D object with 2D object, it should be a length as far as I know...
If you are asking how to transform an area into a length proportional to it, then the standard trick is to build a rectangle having that area and unit height: the length of the base is then the same as the area.
In the picture below, suppose $ABCD$ is your initial rectangle, having area $27/25$. Draw $AE$ of unit length and then $DF$ parallel to $EB$, where $F$ lies on line $AB$. It is immediate that rectangle $AFGE$ has the same area as $ABCD$, beacuse triangles $ABE$, $FGH$ and $CDI$ are equal, and parallelograms $EBID$ and $EBHF$ have base $EB$ in common and equal height. It follows that $AF=27/25$.