A)
[tex]a = 15 \ cm\\d = 17 \ cm\\b = ?\\Obw = ?\\P = ?[/tex]
Z tw. Pitagorasa liczymy drugi bok prostokąta:
[tex]a^{2}+b^{2} = d^{2}\\\\15^{2}+b^{2} = 17^{2}\\\\225 + b^{2} = 289\\\\b^{2} = 289-225 = 64\\\\b = \sqrt{64} = 8 cm\\\\\\Obw = 2a + 2b = 2(a+b)\\\\Obw=2(15+8) \ cm = 2\cdot23 \ cm\\\\\underline{Obw = 46 \ cm}\\\\P = a\cdot b\\\\P = 15 \ cm\cdot8 \ cm\\\\\underline{P = 120 \ cm^{2}}[/tex]
B)
[tex]a = 16 \ cm\\d = 30 \ cm\\b = ?\\Obw = ?\\P = ?\\\\a^{2}+b^{2} = d^{2}\\\\18^{2}+b^{2} = 30^{2}\\\\324 + b^{2} = 900\\\\b^{2} = 900-324 = 576\\\\b = \sqrt{576}=24 \ cm\\\\\\Obw = 2(a+b) =2(18+24)= 2\cdot42 \ cm\\\\\underline{Obw = 84 \ cm}[/tex]
[tex]P = a\cdot b\\\\P = 18 \ cm\cdot24 \ cm\\\\\underline{P = 432 \ cm^{2}}[/tex]
C)
[tex]a = 16 \ cm\\d = 24 \ cm\\b = ?\\Obw = ?\\P = ?\\\\a^{2}+b^{2} = d^{2}\\\\16^{2}+b^{2} = 24^{2}\\\\256+b^{2} = 576\\\\b^{2} = 576-256 = 320\\\\b = \sqrt{320} =\sqrt{64\cdot5} =8\sqrt{5} \ cm\\\\\\Obw = 2a + 2b\\\\Obw=2\cdot16 \ cm + 2\cdot8\sqrt{5} \ cm\\\\\underline{Obw = 16(2+\sqrt{5}) \ cm}[/tex]
[tex]P = a\cdot b\\\\P = 16 \ cm\cdot8\sqrt{5} \ cm\\\\\underline{P = 128\sqrt{5} \ cm^{2}}[/tex]
