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.
 
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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