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11
\(\begin{array}{l}{y^2} = {8^2} + {6^2} = 64 + 36\,\, = 100\,\, \Rightarrow \,\,y = 10\\\\\mathop {ABC}\limits^\Delta \,\,:\,\,\,\,{x^2} + {\left( {3\sqrt 3 } \right)^2} = {\left( {y + 4} \right)^2}\\\\\mathop \Rightarrow \limits^{y = 10} \,\,{x^2} + 27 = {14^2} = 196\, \Rightarrow \,{x^2} = 196 - 27 = 169\\\\ \Rightarrow \,\,x = \sqrt {169} \,\,\, \Rightarrow \,\,\,x = 13\end{array}\)