ГДЗ по геометрии 7 класс Атанасян ФГОС Задание 589

\[\boxed{\mathbf{589.еуроки - ответы\ на\ пятёрку}}\]

\[Рисунок\ по\ условию\ задачи:\]

\[\mathbf{Дан}\mathbf{о:\ }\]

\[\mathrm{\Delta}ABC;\ \]

\[\angle C = 90{^\circ};\]

\[CH\bot AB;\]

\[AC = a;\]

\[CB = b;\]

\[Найти:\]

\[CH - ?\]

\[Решение.\]

\[\textbf{а)}\ a = 5;b = 12:\]

\[1)\ AB = c = \sqrt{144 + 25} =\]

\[= \sqrt{169} = 13;\]

\[2)\ S_{\text{ABC}} = \frac{1}{2}ab = \frac{1}{2} \bullet 5 \bullet 12 = 30;\]

\[S_{\text{ABC}} = \frac{1}{2} \bullet c \bullet CH = 30;\]

\[CH = 30\ :\left( \frac{1}{2} \bullet 13 \right) = \frac{30 \bullet 2}{13} =\]

\[= 4\frac{8}{13}.\]

\[\textbf{б)}\ a = 12;b = 16:\]

\[1)\ AB = c = \sqrt{144 + 256} =\]

\[= \sqrt{400} = 20;\]

\[2)\ S_{\text{ABC}} = \frac{1}{2}ab = \frac{1}{2} \bullet 12 \bullet 16 =\]

\[= 96;\]

\[S_{\text{ABC}} = \frac{1}{2} \bullet c \bullet CH = 96;\]

\[CH = \frac{192}{20} = \frac{96}{10} = 9,6.\]

\[Ответ:а)\ 4\frac{8}{13};\ \ б)\ 9,6.\]