Решебник по геометрии 7 класс Мерзляк Задание 230

\[Схематический\ рисунок.\]

\[Дано:\ \ \]

\[AB = a;\]

\[AC = 2CD;\]

\[CD = 2DB;\]

\[AE = EC;\]

\[CF = FD;\]

\[DT = TB.\]

\[Найти:\]

\[1)\ AF;\]

\[2)\ ET.\]

\[Решение.\]

\[AB = AC + CD + DB = a\]

\[2CD + 2DB + DB = a\]

\[4DB + 3DB = a\]

\[7DB = a\]

\[DB = \frac{a}{7}.\]

\[1)\ AF = AC + CF = 2CD + \frac{1}{2}\text{CD}\]

\[AF = 2,5CD = 5DB = \frac{5a}{7}.\]

\[2)\ ET = EC + CD + DT\]

\[ET = \frac{1}{2}AC + 2DB + \frac{1}{2}\text{DB}\]

\[ET = CD + 2,5DB = 2DB + 2,5DB\]

\[ET = 4,5DB = 4,5 \bullet \frac{a}{7} = \frac{9a}{14}.\]

\[Ответ:\ \ 1)\ \frac{5a}{7};\ 2)\ \frac{9a}{14}.\]