Решебник по геометрии 8 класс Мерзляк Задание 428

\[Схематический\ рисунок.\]

\[Дано:\]

\[\mathrm{\Delta}DEF\sim\mathrm{\Delta}MKT;\]

\[\frac{\text{MK}}{\text{DE}} = \frac{\text{KT}}{\text{EF}};\]

\[MK = 18\ см;\]

\[KT = 16\ см;\]

\[MT = 28\ см;\]

\[MK\ :DE = 4\ :5.\]

\[Найти:\]

\[DE;\ EF;\ DF.\]

\[Решение.\]

\[\frac{\text{KT}}{\text{EF}} = \frac{\text{MT}}{\text{DF}} = \frac{\text{MK}}{\text{DE}} = \frac{4}{5}:\]

\[DE = \frac{5}{4}MK = \frac{5}{4} \bullet 18 = 22,5\ см.\]

\[EF = \frac{5}{4}KT = \frac{5}{4} \bullet 16 = 20\ см.\]

\[DF = \frac{5}{4}MT = \frac{5}{4} \bullet 28 = 35\ см.\]

\[Ответ:\ \ DE = 22,5\ см;\ EF = 20\ см;\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ DF = 35\ см.\]