12 A sculpture formed from a prism is fixed on a horizontal platform, as shown in the diagram. The shape of the cross-section of the sculpture can be modelled by the equation \(x ^ { 2 } + 2 x y + 2 y ^ { 2 } = 10\), where \(x\) and \(y\) are measured in metres. The \(x\) and \(y\) axes are horizontal and vertical respectively.
\includegraphics[max width=\textwidth, alt={}, center]{66b1c52c-0475-493a-8c0a-abf4c2c7b07d-18_214_451_776_858} Find the maximum vertical height above the platform of the sculpture.