Proving that if $a^2+b^2=c^2$, then $a+b\ge c$. Hello, I'm trying to prove this statement.

Let a,b & c be three positive real numbers and if $a^2+b^2=c^2$ then $a+b\ge c$

Any help, please?

$(a+b)^2=a^2+b^2+2ab\geq a^2+b^2= c^2\rightarrow (a+b)^2\geq c^2\rightarrow a+b\geq c$
