The numbers... they look familiar.

Algebra Level 3

If \(a,b,c,d\) are positive real numbers satisfying

\[a+c=5 \text{ and } b+d=12, \]

find the minimum value of \(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } +\sqrt{ { c }^{ 2 }+{ d }^{ 2 } } \)

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