# Practice! #4

Algebra Level 4

$\large \begin{cases} a^{2}+b^{2}=c^{2} \\ \dfrac{ab}{2}=a+b+c \end{cases}$

Positive integers $$a$$, $$b$$ and $$c$$, where $$a<b<c$$, satisfy the system of equations above. If there are $$n$$ triplets $$(a,b,c)$$ then enter $$\displaystyle\sum_{k=1}^{n} (a_{k} + b_{k} + c_{k})$$ as your answer.

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