\[\boxed{\mathbf{472.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}\text{ABC} - прямоугольный;\]
\[\angle C = 90{^\circ};\]
\[S_{\text{ABC}} = 168\ см^{2};\]
\[\frac{\text{AC}}{\text{BC}} = \frac{7}{12}.\]
\[\mathbf{Найти:}\]
\[\text{AC}\ и\ \text{BC}.\]
\[\mathbf{Решение.}\]
\[1)\frac{\text{AC}}{\text{BC}} = \frac{7}{12} \Longrightarrow \text{AC} = \frac{7\text{BC}}{12}.\]
\[2)\ S_{\text{ABC}} = \frac{1}{2} \bullet \text{AC} \bullet \text{CB} =\]
\[= \frac{1}{2} \bullet \frac{7\text{BC}}{12} \bullet \text{BC} = \frac{7}{24}BC^{2} =\]
\[= 168\ см^{2}.\]
\[BC^{2} = 576 \Longrightarrow \text{BC} = 24\ см.\]
\[3)\ \text{AC} = \frac{7\text{BC}}{12} = \frac{7 \bullet 24}{12} = 14\ см.\]
\[Ответ:\text{AC} = 14\ см;\text{BC} = 24\ см.\]