Finding the length of this side of similar figures

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The discussion centers on determining the value of ##x## in similar figures, with participants expressing uncertainty about the sufficiency of the provided information. One contributor mentions that the length EF is 19.8 cm but concludes that ##x## cannot be determined from the given data. Another suggests using a "3, 4, 5" right triangle to approach a solution, but this is met with confusion regarding its relevance to actual lengths versus ratios. Ultimately, it is noted that any arbitrary value for ##x## could yield a corresponding value, indicating a lack of definitive information. The consensus is that the current data is insufficient for a precise calculation of ##x##.
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Is it possible to find the value of ##x##? I feel like the information is not enough to find it.

I have found EF, which is 19.8 cm (if this is helpful)

Thanks
 
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You can't find ##x## from the information given.
 
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Thank you very much PeroK
 
If you made a "3,4, 5" right triangle with 5x as the hypotenuse, you could get closer to a solution.
 
osilmag said:
If you made a "3,4, 5" right triangle with 5x as the hypotenuse, you could get closer to a solution.
Sorry I don't understand. I think what you suggest is related to ratio, not to actual length, or am I mistaken?

Thanks
 
It seems to me that you could make up any value for ##x##, e.g. 3, and then find that some other value, e.g. 5, would work just as well.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
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