# What are some examples of statement-reason format for ratios of segments?

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!

• Do you have any statements in mind? – Julian Mejia Jun 2 at 1:23
• @JulianMejia I'll make one up... Let's say they are in a ratio of 4:1 and the length is 25 (to make it easy) – GeometryPonderer Jun 2 at 1:37

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 $$5$$.
• I guess from my answer you can do it, right? Somtehing like 1. The lengths are of the form $t,4t$ (Reason: Ratio is $4:1$) 2. 4t+t=25(Reason total length is 25)..... and so on. – Julian Mejia Jun 2 at 2:09