Korzystam z Tw. Pitagorasa aby obliczyć h:
[tex]a^{2} =h^{2} +4^{2} ~~\land ~~h= \frac{3}{5} a\\\\a^{2} =( \frac{3}{5} a)^{2} +4^{2}\\\\a^{2} =\frac{9}{25} a^{2}+16\\\\a^{2} -\frac{9}{25} a^{2}=16\\\\\frac{16}{25} a^{2}=16~~\mid \div \frac{16}{25}\\\\a^{2} =25~~\land ~~a > 0~\Rightarrow ~~a=5\\\\h= \frac{3}{5} a ~~\land ~~a=5~~\Rightarrow ~~h=3~~cm\\\\P_{\Delta ABC} =\dfrac{1}{2} \cdot \mid AB \mid \cdot h~~\land ~~\mid AB \mid = 8~cm~~\land ~~h=3~cm\\\\P_{\Delta ABC} =\dfrac{1}{2} \cdot 8~cm \cdot 3~cm\\\\P_{\Delta ABC} =12~cm^{2}[/tex]
