Решебник по геометрии 8 класс Мерзляк Задание 430

\[Схематический\ рисунок.\]

\[Дано:\]

\[DE \parallel AC;\]

\[\mathrm{\Delta}DBE\sim\mathrm{\Delta}ABC.\]

\[Решение.\]

\[1)\ AB = 16\ см;AC = 20\ см;\]

\[DE = 15\ см:\]

\[\frac{\text{BD}}{\text{AB}} = \frac{\text{DE}}{\text{AC}}\text{\ \ \ }\]

\[BD = \frac{AB \bullet DE}{\text{AC}}\]

\[BD = \frac{16 \bullet 15}{20} = 4 \bullet 3 = 12\ см.\]

\[2)\ AB = 28\ см;BC = 63\ см;\]

\[BE = 27\ см:\]

\[\frac{\text{BD}}{\text{AB}} = \frac{\text{BE}}{\text{BC}}\text{\ \ }\]

\[BD = \frac{AB \bullet BE}{\text{BC}}\]

\[BD = \frac{28 \bullet 27}{63} = 4 \bullet 3 = 12\ см.\]

\[AD = AB - BD = 16\]

\[Ответ:\ \ 1)\ 12\ см;\ 2)\ 16\ см.\]