Question 832143
Show a clear listing of what you know.
-
side 1, 4 cm, the height
side 2, x cm, unknown
side 3, h cm, the hypotenuse, unknown
p = perimeter, taken as known, maybe.
{{{p=4+x+h}}} ---- understand perimeter
{{{x^2+4^2=h^2}}} ----Pythagorean Theorem


You wanted h as a function of p.  Maybe two ways to do it.  Try to find a way to equate expressions for either {{{x}}}, or {{{x^2}}}.  Then solve for h from that.


Note, I did not solve this; I only suggested a way to try.