Divide two segments (lines)

Question

I have two lines with length of A and B. I need to find the line with length of C where C = A/B. C=A/B

For solution i can use any geometric laws (a ruler and a compass). Ultimate idea is that i can divide two real planks one into another and get a third plank. There is a way to multiply two lines but i didnt find a solution to divide them.

Answer 1

Let $AB=x$ and $AC=y$. In this case, $\frac xy=2$, but you can't construct a line segment of length $2$ with no sense of units. So let $AD=1$. Construct a line through $D$ parallel to $\overline{BC}$ that crosses $\overline{AB}$ at $E$. Then $\frac{AB}{AC}=\frac{AE}{AD}=AE$.