They all are squared

Algebra Level 5

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

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