Korzystamy z twierdzenia Pitagorasa:
a² + b² = c²
gdzie:
a,b - przyprostokątne
c - przeciwprostokątna
2.
a)
[tex]a = 21\\b = 20\\\\21^{2}+20^{2} = c^{2}\\\\441 + 400 = c^{2}\\\\c^{2} = 841\\\\c = \sqrt{841}\\\\c = 29\\\\P = \frac{1}{2}ah = \frac{1}{2}\cdot21\cdot20 =21\cdot10 = 210\\\\Obw = a+b+c = 21+20+29 = 70[/tex]
b)
[tex]a = 24\\b = 7\\\\24^{2}+7^{2} = c^{2}\\\\576 + 49 = c^{2}\\\\c^{2} = 625\\\\c = \sqrt{625}\\\\c = 25\\\\P = \frac{1}{2}ah = \frac{1}{2}\cdot24\cdot7 = 12\cdot 7 = 84\\\\Obw = a+b+c = 24+7+25 = 56[/tex]
c)
[tex]a = 4\\b = 2\\\\4^{2}+2^{2} = c^{2}\\\\16+4 = c^{2}\\\\c^{2} = 20\\\\c = \sqrt{20} = \sqrt{4\cdot 5}\\\\c = 2\sqrt{5}\\\\P = \frac{1}{2}ah = \frac{1}{2}\cdot4\cdot2 = 4\\\\Obw = a+b+c = 4+2+2\sqrt{5} = 6+2\sqrt{5}[/tex]
