\[\boxed{\mathbf{538.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}\text{ABC};\]
\[\angle\text{BAD} = \angle\text{DAC};\]
\[\text{CD} = 4,5\ см;\]
\[\text{BD} = 13,5\ см;\]
\[P_{\text{ABC}} = 42\ см.\]
\[\mathbf{Найти:}\]
\[\text{AB} - ?\]
\[\text{AC} - ?\]
\[\mathbf{Решение.}\]
\[1)\ \text{BC} = \text{BD} + \text{DC} =\]
\[= 13,5 + 4,5 = 18\ см.\]
\[2)\ \text{AB} + \text{AC} = P_{\text{ABC}} - \text{BC} =\]
\[= 42 - 18 = 24\ см.\]
\[3)\ \angle\text{BAD} = \angle\text{DAC}\ (по\ условию):\]
\[\frac{\text{BD}}{\text{DC}} = \frac{\text{AB}}{\text{AC}} = \frac{13,5}{4,5} = 3\]
\[\text{AB} = 3\text{AC}.\]
\[4)\ 3\text{AC} + \text{AC} = 24\]
\[4\text{AC} = 24\]
\[\text{AC} = 6\ см.\]
\[5)\ \text{AB} = 3 \bullet 6 = 18\ см.\]
\[\mathbf{Ответ:}\text{AB} = 18\mathbf{\ см};\text{AC} = 6\ см.\]