\[\boxed{\mathbf{253\ (253)}\mathbf{.}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \frac{8}{19} < \frac{x}{19} < 1\ \ \ \ \]
\[x = 9,\ 10,\ 11,\ 12,\ 13,\ 14,\ 15,\ 16,\ \]
\[17,\ 18.\]
\[2)\ \frac{1}{3} < \frac{x}{18} < \frac{5}{6}\text{\ \ \ }\]
\[\frac{6}{18} < \frac{x}{18} < \frac{15}{18}\text{\ \ \ \ }\]
\[x = 7,\ 8,\ 9,\ 10,\ 11,\ 12,\ 13,\ 14.\]
\[\boxed{\mathbf{253}\mathbf{.}}\]
\[P_{\text{ABC}} = 27\ см;\]
\[P_{\text{ADC}} = 22\ см;\]
\[P_{\text{ABCD}} = 31\ см;\]
\[AC - ?\]
\[P_{\text{ABCD}} = P_{\text{ABC}} + P_{\text{ADC}} - 2AC\]
\[31 = 27 + 22 - 2AC\]
\[49 - 2AC = 31\]
\[2AC = 49 - 31\]
\[2AC = 18\]
\[AC = 18\ :2 = 9\ см.\]
\[Ответ:9\ см.\]