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I do not get the following formulas :

  • The minimum perimeter of any triangle (abc), given the heights corresponding to the a and b-sides.

  • The maximum height corresponding to the side b of any triangle (abc), given the value of its perimeter and height corresponding to the a-side.


marked as duplicate by Zev Chonoles, AlexR, Joel Reyes Noche, user99914, user147263 May 27 '15 at 0:49

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migrated from mathoverflow.net May 26 '15 at 21:01

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  • $\begingroup$ Do not cross-post such questions to mathoverflow, it's about research-level mathematics. $\endgroup$ – AlexR May 26 '15 at 21:06
  • Given the length of two sides $a$ and $b$ (taking $a \ge b$), the perimeter $p$ is constrained by $2a < p < 2(a+b)$.

  • Given the length of one side $a$ and the value of the perimeter $p$, the length of a remaining side $b$ is constrained by $\dfrac{p-2a}{2} < b < \dfrac{p}{2} $ and also by $0<b< p-a$.

  • $\begingroup$ OK, that might be better answered in the duplicate question then. Sorry for the misunderstanding. If I think of a bound which is still worthwhile but lower complexity, I'll update my answer. $\endgroup$ – Joffan May 28 '15 at 5:47

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