$a,b$ 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 $\text{DEF}?$
- It is an acute-angled triangle
- It is an right-angled triangle
- It is an obtuse-angled triangle
- None of the above