Odpowiedź:
zad. 4
[tex]a) {4}^{2} + {5}^{2} = {x}^{2} \\ 16 + 25 = {x}^{2} \\ {x}^{2} = 41 \\ x = \sqrt{41} [/tex]
[tex]P = ( { \sqrt{41} )}^{2} = 41[/tex]
b)
[tex] {x}^{2} + {7}^{2} = {10}^{2} \\ {x}^{2} + 49 = 100 \\ {x}^{2} = 51 \\ x = \sqrt{51} \\ P = ( \sqrt{51} {)}^{2} = 51[/tex]
c)
[tex] {10}^{2} + {x}^{2} = {11}^{2} \\ 100 + {x}^{2} = 121 \\ {x}^{2} = 21 \\ x = \sqrt{21} \\ P = ( \sqrt{21} {)}^{2} = 21[/tex]
zad. 5
[tex]a) {b}^{2} + {20}^{2} = {25}^{2} \\ {b}^{2} + 400 = 625 \\ {b}^{2} = 225 \\ b = 15[/tex]
[tex]b) {30}^{2} + {40}^{2} = {x}^{2} \\ 900 + 1600 = {x}^{2} \\ {x}^{2} = 2500 \\ x = 50[/tex]
[tex]c) {4}^{2} + {p}^{2} = {6}^{2} \\ 16 + {p}^{2} = 36 \\ {p}^{2} = 20 \\ p = \sqrt{20} = 2 \sqrt{5} [/tex]
[tex]d) {6}^{2} + {5}^{2} = {m}^{2} \\ 36 + 25 = {m}^{2} \\ {m}^{2} = 51 \\ m = \sqrt{51} [/tex]
[tex]e) {w}^{2} + {5}^{2} = {13}^{2} \\ {w}^{2} + 25 = 169 \\ {w}^{2} = 144 \\ w = 12[/tex]
