\[\boxed{\mathbf{590.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}ABC;\]
\[AB = BC = 10\ см;\]
\[AC = 12\ см.\]
\[\mathbf{Найти:}\]
\[AM;CL;BN.\]
\[\mathbf{Решение.}\]
\[1)\ По\ формуле\ Герона\ \]
\[\left( p = \frac{a + b + c}{2} \right):\]
\[S_{\text{ABC}} = \sqrt{p(p - a)(p - b)(p - c)};\]
\[p = \frac{10 + 10 + 12}{2} = 16\ см.\]
\[2)\ S_{\text{ABC}} = \frac{1}{2} \bullet BC \bullet AM = 48\]
\[\frac{1}{2} \bullet 10 \bullet AM = 48\]
\[AM = \frac{48}{5} = 9\frac{3}{5} = 9,6\ см.\]
\[3)\ S_{\text{ABC}} = \frac{1}{2} \bullet AB \bullet LC = 48\]
\[\frac{1}{2} \bullet 10 \bullet LC = 48\]
\[LC = \frac{48}{5} = 9\frac{3}{5} = 9,6\ см.\]
\[4)\ S_{\text{ABC}} = \frac{1}{2} \bullet AC \bullet BN = 48\]
\[\frac{1}{2} \bullet 12 \bullet BN = 48\]
\[BN = \frac{48}{6} = 8\ см.\]
\[\mathbf{Ответ}:AM = 9\ см;LC = 9\ см;\]
\[BN = 8\ см\mathbf{.}\]