Решебник по геометрии 7 класс Мерзляк Задание 34

\[Схематический\ рисунок.\]

\[Дано:\ \ \]

\[AB = 20\ см;\]

\[1)\ AC = BC + 5\ см;\]

\[2)\ AC = BC\ :4;\]

\[3)\ AC\ :BC = 9\ :11.\]

\[Найти:\]

\[AC;\ BC.\]

\[Решение.\]

\[AB = AC + BC\]

\[1)\ 20 = BC + 5 + BC\]

\[2BC = 15\]

\[BC = 7,5\]

\[AC = 7,5 + 5 = 12,5\ см.\]

\[2)\ 20 = \frac{\text{BC}}{4} + BC\ \ \ | \cdot 4\]

\[80 = BC + 4BC\]

\[5BC = 80;\]

\[BC = 16\ см.\]

\[AC = \frac{16}{4} = 4\ см.\]

\[3)\ AC = \frac{9}{11}BC:\]

\[20 = \frac{9}{11}BC + BC\]

\[220 = 9BC + 11BC\]

\[20BC = 220\]

\[BC = 11\ см.\]

\[AC = \frac{9}{11} \bullet 11 = 9\ см.\]

\[Ответ:\ \ 1)\ 12,5\ см,\ 7,5\ см;\ \]

\(2)\ 4\ см,\ 16\ см;\ 3)\ 9\ см,\ 11\ см.\)