a)
[tex] {3}^{2} + {3}^{2} = {x}^{2} \\ 9 + 9 = {x}^{2} \\ {x}^{2} = 18 \\ x = \sqrt{18} = \sqrt{9 \times 2} = 3 \sqrt{2} [/tex]
b)
[tex] {x}^{2} + {15}^{2} = {17}^{2} \\ {x}^{2} + 225 = 289 \\ {x}^{2} = 64 \\ x = \sqrt{64} = 8[/tex]
c)
[tex] {x}^{2} + {3}^{2} = ( \sqrt{13} {)}^{2} \\ {x}^{2} + 9 = 13 \\ {x}^{2} = 4 \\ x = \sqrt{4} = 2[/tex]
d)
[tex](7.5 {)}^{2} + {x}^{2} = (12.5 {)}^{2} \\ 56.25 + {x}^{2} = 156.25 \\ {x}^{2} = 100 \\ x = \sqrt{100} = 10[/tex]
