Odpowiedź:
Na początek musimy obliczyć niewiadoma ze wzoru Pitagorasa
a)
[tex]2 {( 2\sqrt{2} )}^{2} = {x}^{2} \\ 2 \times 4 \times 2 = {x}^{2} \\ 8 \times 2 = {x}^{2} \\ 16 = {x}^{2} \\ \sqrt{16} = \sqrt{ {x}^{2} } \\ 4 = x[/tex]
[tex]Ob = 2 \sqrt{2} + 2 \sqrt{2} + 4 = 4 \sqrt{2} + 4[/tex]
b)
[tex] {3}^{2} + {3}^{2} = {x}^{2} \\ 2 \times {3}^{2} = {x}^{2} \\ 2 \times 9 = {x}^{2} \: \\ 18 = {x}^{2} \\ \sqrt{18} = \sqrt{ {x}^{2} } \\ 3 \sqrt{2} = x[/tex]
[tex]Ob = 3 + 3 + 3 \sqrt{2} = 6 + 3 \sqrt{2} [/tex]
c)
[tex]2 {x}^{2} = {12}^{2} \\ 2 {x}^{2} = 144 \: \: \: \: \: | \div 2 \\ {x}^{2} = 72 \\ \sqrt{ {x}^{2} } = \sqrt{72} \\ x = 6 \sqrt{2} [/tex]
[tex]Ob = 12 + 6 \sqrt{2} + 6 \sqrt{2} = 12 + 12 \sqrt{2} [/tex]
