# System of Equations

**Algebra**Level 4

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

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