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We can find an acute triangle with the three altitude lengths 1, 3, and h, if and only if h^2 belongs to interval (p,q). Find (p, q).

 May 18, 2021
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The three sides are (Letting area be K) \(\frac{2K}{3}, \frac{2K}{1}, \frac{2K}{h}\).

 

Then, simply do triangle inequality with cases depending on how big \(\frac{2K}{h}\) is.

 May 19, 2021

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