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!

  • $\begingroup$ Do you have any statements in mind? $\endgroup$ – Julian Mejia Jun 2 at 1:23
  • $\begingroup$ @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) $\endgroup$ – 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 $5$.

  • $\begingroup$ Could you please put that into statement reason format, thanks for a great answer! $\endgroup$ – GeometryPonderer Jun 2 at 1:56
  • $\begingroup$ @GeometryPonderer just to clarify. Statement Reason format means that you put some statement and its reason next to it? $\endgroup$ – Julian Mejia Jun 2 at 2:05
  • $\begingroup$ That is right! You may need to use an external software and take a screenshot if you do decide to do it $\endgroup$ – GeometryPonderer Jun 2 at 2:07
  • $\begingroup$ 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. $\endgroup$ – Julian Mejia Jun 2 at 2:09
  • $\begingroup$ @JulianMenjia Alright, thanks for your time! $\endgroup$ – GeometryPonderer Jun 2 at 2:16

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