\[\boxed{\mathbf{604.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}ABC\sim\mathrm{\Delta}A_{1}B_{1}C_{1};\]
\[AB = 6\ см;\]
\[AC = 10\ см;\]
\[BC = 9\ см;\]
\[A_{1}C_{1} = 7,5\ см.\]
\[\mathbf{Найти:}\]
\[A_{1}B_{1} - ?\]
\[B_{1}C_{1} - ?\]
\[\mathbf{Решение.}\]
\[1)\ \mathrm{\Delta}ABC\sim\mathrm{\Delta}A_{1}B_{1}C_{1}\ \]
\[(по\ условию):\]
\[\frac{\text{AB}}{A_{1}B_{1}} = \frac{\text{AC}}{A_{1}C_{1}} = \frac{\text{BC}}{B_{1}C_{1}} = k;\]
\[2)\ \frac{6}{A_{1}B_{1}} = \frac{9}{B_{1}C_{1}} = \frac{10}{7,5} = k\]
\[\ k = \frac{10}{7,5} = \frac{4}{3}.\]
\[3)\ \frac{6}{A_{1}B_{1}} = \frac{4}{3}\]
\[4A_{1}B_{1} = 6 \bullet 3\]
\[A_{1}B_{1} = \frac{6 \bullet 3}{4} = 4,5\ см.\]
\[4)\ \frac{9}{B_{1}C_{1}} = \frac{4}{3}\]
\[4B_{1}C_{1} = 9 \bullet 3.\]
\[B_{1}C_{1} = \frac{27}{4} = 6,75\ см.\]
\[\mathbf{Ответ:}A_{1}B_{1} = 4,5\ см;\ \]
\[B_{1}C_{1} = 6,75\ см.\]