Решебник по геометрии 9 класс Мерзляк Задание 129

\[Схематический\ рисунок.\]

\[Дано:\]

\[\mathrm{\Delta}ABC\sim\mathrm{\Delta}A_{1}B_{1}C_{1};\]

\[AB = 8\ см;\ \]

\[A_{1}B_{1} = 5\ см;\]

\[P_{A_{1}B_{1}C_{1}} = P_{\text{ABC}} - 18\ см.\]

\[Найти:\]

\[P_{\text{ABC}};\ P_{A_{1}B_{1}C_{1}}.\]

\[Решение.\]

\[В\ \mathrm{\Delta}\text{ABC\ }и\ \mathrm{\Delta}A_{1}B_{1}C_{1}:\]

\[k = \frac{P_{\text{ABC}}}{P_{A_{1}B_{1}C_{1}}} = \frac{\text{AB}}{A_{1}B_{1}} = \frac{8}{5};\]

\[\frac{P_{\text{ABC}}}{P_{\text{ABC}} - 18} = \frac{8}{5}\text{\ \ }\]

\[5P_{\text{ABC}} = 8P_{\text{ABC}} - 144\]

\[3P_{\text{ABC}} = 144\ \ \ \]

\[P_{\text{ABC}} = 48\ см.\]

\[P_{A_{1}B_{1}C_{1}} = 48 - 18 = 30\ см.\]

\[Ответ:\ \ 30\ см;\ 48\ см.\]