\[\boxed{\mathbf{549.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}\text{ABC}\sim\mathrm{\Delta}A_{1}B_{1}C_{1};\]
\[\text{AB} = 30\ см;\]
\[\text{BC} = 20\ см;\]
\[\text{AC} = 15\ см;\]
\[P_{A_{1}B_{1}C_{1}} = 26\ см.\]
\[\mathbf{Найти:}\]
\[A_{1}B_{1};B_{1}C_{1};A_{1}C_{1}.\]
\[\mathbf{Решение.}\]
\[1)\ P_{\text{ABC}} = \text{AB} + \text{BC} + \text{AC} =\]
\[= 30 + 20 + 15 = 65\ см.\]
\[2)\frac{P_{\text{ABC}}}{P_{A_{1}B_{1}C_{1}}} = \frac{65}{26} = 2,5 \Longrightarrow k = 2,5.\]
\[3)\frac{\text{AB}}{A_{1}B_{1}} = \frac{\text{BC}}{B_{1}C_{1}} = \frac{\text{AC}}{A_{1}C_{1}} = 2,5.\]
\[4)\ \text{AB} = 2,5 \bullet A_{1}B_{1} \Longrightarrow\]
\[\Longrightarrow A_{1}B_{1} = \frac{30}{2,5} = 12\ см.\]
\[\text{BC} = 2,5 \bullet B_{1}C_{1} \Longrightarrow\]
\[\Longrightarrow B_{1}C_{1} = \frac{20}{2,5} = 8\ см.\]
\[\text{AC} = 2,5 \bullet A_{1}C_{1} \Longrightarrow\]
\[\Longrightarrow A_{1}C_{1} = \frac{15}{2,5} = 6\ см.\]
\[\mathbf{Ответ:}A_{1}B_{1} = 12\ см;\]
\[B_{1}C_{1} = 8\ см;A_{1}C_{1} = 6\ см\mathbf{.}\]