They all are squared

Algebra Level 4

\[\large \begin{cases}a^2+ab+b^2=25 \\ b^2+bc+c^2=49 \\ c^2+ca+a^2=64\end{cases}\]

Let \(a\), \(b\), and \(c\) be positive real numbers which satisfy the above system of equation. Find \((a+b+c)^2\).