\[\boxed{\text{207\ (207).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\frac{a + 2b}{a} = 11\ \ \ \ \ \ \ | \cdot a\]
\[a + 2b = 11a\]
\[2b = 11a - a\]
\[2b = 10a\]
\[b = \frac{10a}{2}\]
\[b = 5a.\]
\[Подставим:\]
\[\frac{(a - 3b)^{2}}{b^{2}} = \frac{(a - 3 \cdot 5a)^{2}}{(5a)^{2}} =\]
\[= \frac{(a - 15a)^{2}}{25a^{2}} = \frac{( - 14{a)}^{2}}{25a^{2}} =\]
\[= \frac{196a^{2}}{25a^{2}} = \frac{196}{25} = 7,84.\]
\[Ответ:7,84.\]