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Geometry Level 5

\[\begin{cases} { x }^{ 2 } + \dfrac { { y }^{ 2 } }{ 3 } + xy = 25 \\ \dfrac { { y }^{ 2 } }{ 3 } + { z }^{ 2 } = 9 \\ { z }^{ 2 } + {x }^{ 2 } + zx = 16\end{cases} \]

Positive reals \(x\), \(y\) and \(z\) satisfy the system of equations above. Find \((xy + 2yz + 3zx)\times \sqrt { 3 }\).

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