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$a,b$ and $c$ are the lengths of the triangle $\text{ABC}$ and $d,e$ and $f$ are the lengths of the sides of the triangle $\text{DEF}$. If the following equations hold true:

• $a(a+b+c)=d^2$
• $b(a+b+c)=e^2$
• $c(a+b+c)=f^2$

then which of the following is always true of triangle $\text{DEF}?$

1. It is an acute-angled triangle
2. It is an right-angled triangle
3. It is an obtuse-angled triangle
4. None of the above

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