Решебник по геометрии 9 класс Мерзляк Задание 144

\[1)\ \ 5\ см,\ \ \ 5\ см,\ \ \ 6\ см:\]

\[p = \frac{1}{2}(5 + 5 + 6) = \frac{1}{2} \bullet 16 = 8;\]

\[S = \sqrt{8(8 - 5)(8 - 5)(8 - 6)} =\]

\[= \sqrt{8 \bullet 3 \bullet 3 \bullet 2} = \sqrt{144} = 12\ см^{2}.\]

\[R = \frac{\text{abc}}{4S} = \frac{5 \bullet 5 \bullet 6}{4 \bullet 12} = 3,125\ см;\]

\[r = \frac{S}{p} = \frac{12}{8} = \frac{3}{2} = 1,5\ см.\]

\[Ответ:\ \ 1,5\ см;\ 3,125\ см.\]

\[2)\ \ 25\ см,\ \ \ 29\ см,\ \ \ 36\ см:\]

\[p = \frac{1}{2}(25 + 29 + 36) =\]

\[= \frac{1}{2} \bullet 90 = 45;\]

\[S = \sqrt{45(45 - 25)(45 - 29)(45 - 36)};\]

\[S = \sqrt{45 \bullet 20 \bullet 16 \bullet 9} =\]

\[= \sqrt{129\ 600} = 360\ см^{2}.\]

\[R = \frac{\text{abc}}{4S} = \frac{25 \bullet 29 \bullet 36}{4 \bullet 360} = \frac{145}{8} =\]

\[= 18,125\ см;\]

\[r = \frac{S}{p} = \frac{360}{45} = 8\ см.\]

\[Ответ:\ \ 8\ см;\ 18,125\ см.\]