Решебник по геометрии 9 класс Мерзляк Задание 50

\[Дано:\]

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

\[AB = 15\ см;\]

\[BC = 35\ см;\]

\[\angle A = 120{^\circ}.\]

\[Решение.\]

\[BC^{2} = AB^{2} + AC^{2} - 2AB \bullet AC \bullet \cos{\angle A}\]

\[1225 = 225 + AC^{2} + 2 \bullet 15 \bullet AC \bullet \frac{1}{2}\]

\[AC^{2} + 15AC - 1000 = 0\]

\[D = 15^{2} + 4 \bullet 1000 =\]

\[= 225 + 4000 = 4225\]

\[AC_{1} = \frac{- 15 - 65}{2} = - 40;\]

\[AC_{2} = \frac{- 15 + 65}{2} = 25\ см.\]

\[P_{\text{ABC}} = AB + BC + AC =\]

\[= 15 + 35 + 25 = 75\ см.\]

\[Ответ:\ \ 75\ см.\]