I'm developing a web application that consists of a calculator triangles. Although I am not a mathematician, with paper, derive and Geogebra I managed to get a lot of formulas to calculate a triangle with the minimum number of data possible. Maybe some is unpublished, and limits to be introduced only correct data.
I do not get the following formulas :
The minimum perimeter of any triangle (abc) once known the heights corresponding to the $a$ and $b$-sides.
The maximum height corresponding to the side $b$ of any triangle (abc) once known the value of its perimeter and height corresponding to the $a$-side.
I am looking for an answer in a way that could be implemented in php (programming language).