ГДЗ по геометрии 9 класс Атанасян Задание 484

\[\boxed{\mathbf{484.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\mathbf{Теорема\ Пифагора:}\]

\[a^{2} + b^{2} = c^{2};\]

\[где\ a\ и\ b - катеты;\]

\[c - гипотенуза.\]

\[Выразим\ b:\]

\[b^{2} = c^{2} - a^{2}.\]

\[\textbf{а)}\ a = 12;c = 13:\]

\[b^{2} = 169 - 144 = 25\]

\[b = 5.\]

\[\textbf{б)}\ a = 7;c = 9:\]

\[b^{2} = 81 - 49 = 32\]

\[b = \sqrt{32} = 4\sqrt{2}.\]

\[\textbf{в)}\ a = 12;c = 2b:\]

\[b^{2} = 4b^{2} - 144\]

\[3b^{2} = 144\]

\[b^{2} = 48\]

\[b = 4\sqrt{3}.\]

\[\textbf{г)}\ a = 2\sqrt{3};c = 2b:\]

\[b^{2} = 4b^{2} - 12\]

\[3b^{2} = 12\]

\[b^{2} = 4\]

\[b = 2.\]

\[\textbf{д)}\ a = 3b;c = 2\sqrt{10}:\]

\[b^{2} = 40 - 9b^{2}\]

\[10b^{2} = 40\]

\[b^{2} = 4\]

\[b = 2.\]