Step-by-step explanation:
Pythagorean Theorem
1.[tex]c = \sqrt{(3)^{2} + {(4)}^{2} } \\ c = \sqrt{9 + 16} \\ c = \sqrt{25} \\ c = 5[/tex]
2.
[tex] {(12)}^{2} = {(8)^{2} + {(a)}^{2} } \\ 144=64 + {a}^{2} \\ \sqrt{144 - 64} = a \\ a =4 \sqrt{5} [/tex]
3.
[tex] {(24)}^{2} = {(18)^{2} + {(a)}^{2} } \\ 576=324 + {a}^{2} \\ \sqrt{576 - 324} = a \\ a =6 \sqrt{7} [/tex]
4.
[tex] {(15)}^{2} = {(9)^{2} + {(a)}^{2} } \\ 225=81+ {a}^{2} \\ \sqrt{225- 81} = a \\ a = 12[/tex]
5.
[tex]c = \sqrt{(4)^{2} + {(6)}^{2} } \\ c = \sqrt{16 + 36} \\ c = 2\sqrt{13}[/tex]
