Odpowiedź:
a)
[tex](\sqrt{2})^{2}+(\sqrt{3})^{2}=c^{2}\\ 2+3=c^{2}\\ 5=c^{2}\\ c=\sqrt{5}\\ P=\frac{1}{2}.\sqrt{2}.\sqrt{3}=\frac{\sqrt{6} }{2} \\ Obw=\sqrt{2}+\sqrt{3}+\sqrt{5}[/tex]
b)
[tex]2^{2}+(2\sqrt{3})^{2}=c^{2}\\ 4+4x 3=c^{2}\\ 4+12=c^{2}\\ 16=c^{2}\\ c=\sqrt{16}=4\\ P=\frac{1}{2} x2x2\sqrt{3}=2\sqrt{3}\\ Obw=2+2\sqrt{3}+4=6+2\sqrt{3} \\[/tex]
c)
[tex](5\sqrt{2} )^{2}+(5\sqrt{2} )^{2}=c^{2}\\ 25x2+25x2=c^{2}\\ 50+50=c^{2}\\ 100=c^{2}\\ c=\sqrt{100}=10\\ P=\frac{1}{2}x5\sqrt{2}x5\sqrt{2}=\frac{5\sqrt{2}x5\sqrt{2} }{2}=\frac{25x2}{2}=25\\ Obw=2x5\sqrt{2}+10=10\sqrt{2}+10[/tex]
Szczegółowe wyjaśnienie:
