\[\boxed{\mathbf{470.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}\text{ABC};\]
\[\text{AB} = 7,5\ см;\]
\[\text{BC} = 3,2\ см;\]
\[\text{CH} = 2,4\ см;\]
\[\text{AB}\bot\text{CH};\]
\[\text{AE}\bot\text{BC}.\]
\[\mathbf{Найти:}\]
\[\text{AE} - ?\]
\[\mathbf{Решение.}\]
\[1)\ S_{\text{ABC}} = \frac{1}{2} \bullet \text{AB} \bullet \text{CH} =\]
\[= \frac{1}{2} \bullet 7,5 \bullet 2,4 = 9\ см^{2}.\]
\[2)\ S_{\text{ABC}} = \frac{1}{2} \bullet \text{BC} \bullet \text{AE} =\]
\[= \frac{1}{2} \bullet 3,2 \bullet \text{AE} = 9\ см^{2}.\]
\[3)\ \text{AE} = \frac{9 \bullet 2}{3,2} = 5,625\ см.\]
\[Ответ:5,625\ см.\]