# The minimum perimeter and maximum height of a triangle under constraints [duplicate]

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.

## migrated from mathoverflow.netMay 26 '15 at 21:01

This question came from our site for professional mathematicians.

• Do not cross-post such questions to mathoverflow, it's about research-level mathematics. – 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 $0<b< p-a$.