[tex]a^{2}+b^{2} = c^{2} \\c= \sqrt{a^{2}+b^{2} } \\ P = \frac{1}{2} a*b\ = \frac{1}{2} h_{c} *c\\ \frac{1}{2} a*b\ = \frac{1}{2} h_{c}* \sqrt{a^{2}+b^{2} }\\[/tex]
[tex]\frac{1}{2} h_{c}= \frac{ \frac{1}{2} a*b}{\sqrt{a^{2}+b^{2} } } *2\\h_{c}= \frac{ab}{\sqrt{a^{2}+b^{2} } }[/tex]
