\[\boxed{\mathbf{484.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\mathbf{Теорема\ Пифагора:}\]
\[a^{2} + b^{2} = c^{2};\]
\[где\ a\ и\ b - катеты;\]
\[c - гипотенуза.\]
\[Выразим\ b:\]
\[b^{2} = c^{2} - a^{2}.\]
\[\textbf{а)}\ a = 12;c = 13:\]
\[b^{2} = 169 - 144 = 25\]
\[b = 5.\]
\[\textbf{б)}\ a = 7;c = 9:\]
\[b^{2} = 81 - 49 = 32\]
\[b = \sqrt{32} = 4\sqrt{2}.\]
\[\textbf{в)}\ a = 12;c = 2b:\]
\[b^{2} = 4b^{2} - 144\]
\[3b^{2} = 144\]
\[b^{2} = 48\]
\[b = 4\sqrt{3}.\]
\[\textbf{г)}\ a = 2\sqrt{3};c = 2b:\]
\[b^{2} = 4b^{2} - 12\]
\[3b^{2} = 12\]
\[b^{2} = 4\]
\[b = 2.\]
\[\textbf{д)}\ a = 3b;c = 2\sqrt{10}:\]
\[b^{2} = 40 - 9b^{2}\]
\[10b^{2} = 40\]
\[b^{2} = 4\]
\[b = 2.\]