I'm wondering what some examples might be for a proof (statement/reason format) that required you to find the length of two segments if you know that their ratio is $x:y$ and that the total length is $z$.
If I could have some examples that'd be great, thanks!
So, I will use your example given in the comments. suppose the problem is the following: We have two segments with length ratio $4:1$ and the total length combined is $25$. What are the lengths of these segments?
Solution: Since the ratio is $4:1$ we can express the lengths as $4t$ and $t$. Since the total length is $25$, we have $4t+t=25$. We solve for $t$, getting $t=5$. So the lengths were $4(5)=20$ and $5$.