Zad. 2
Dane:
p, a
Obl. P całkowite
a\sqrt2=d/:\sqrt2
a=\frac{d}{\sqrt2}
a^2+h^2=p^2
(\frac{d}{\sqrt2})^2+h^2=p^2
\frac{d^2}{2}+h^2=p^2
h^2=p^2-\frac{d^2}{2}
h=\sqrt{p^2-\frac{d^2}{2}}
h=\sqrt{\frac{2p^2-d^2}{2}}
h=\frac{\sqrt{2p^2-d^2}}{\sqrt2}
P_c=2a^2+4*a*h=2*(\frac{d}{\sqrt2})^2+4*\frac{d}{\sqrt2}*\frac{\sqrt{2p^2-d^2}}{\sqrt2}=
=\frac{2d^2}{2}+\frac{4d\sqrt{2p^2-d^2}}{2}=d^2+2d\sqrt{2p^2-d^2}=
=d(d+2\sqrt{2p^2-d^2})