\[\boxed{\mathbf{469.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}\text{ABC};\]
\[\text{AB} = 16\ см;\]
\[\text{BC} = 22\ см;\]
\[\text{CH} = 11\ см;\]
\[\text{AB}\bot\text{CH};\]
\[\text{AE}\bot\text{BC}.\]
\[\mathbf{Найти:}\]
\[\text{AE} - ?\]
\[\mathbf{Решение.}\]
\[1)\ S_{\text{ABC}} = \frac{1}{2} \bullet \text{AB} \bullet \text{CH} =\]
\[= \frac{1}{2} \bullet 16 \bullet 11 = 88\ см^{2}.\]
\[2)\ S_{\text{ABC}} = \frac{1}{2} \bullet \text{BC} \bullet \text{AE} =\]
\[= \frac{1}{2} \bullet 22 \bullet \text{AE} = 88\ см^{2}.\]
\[3)\ \text{AE} = \frac{88 \bullet 2}{22} = 8\ см.\]
\[Ответ:8\ см.\]