Let $a, b$ and $c$ be the lengths of the sides of an arbitrary triangle. Pick out the true statements. Let $a, b$ and $c$ be the lengths of the sides of an arbitrary triangle. Define
$$x =\frac{ab + bc + ca}{a^2 + b^2 + c^2}.$$
Pick out the true statements.
(a) $1/2 ≤ x ≤  2$.
(b) $1/2 ≤ x ≤  1$.
(c) $1/2 < x ≤  1$.    
How can I able to solve this problem

We know in every triangle $ABC$ there are some useful relations called Law of cosines:
$$a^2=b^2+c^2-2bc\cos(A)\\b^2=a^2+c^2-2ac\cos(B)\\c^2=a^2+b^2-2ab\cos(C)$$ By adding them we have: $$a^2+b^2+c^2=2(bc\cos(A)+ac\cos(B)+ab\cos(C))$$ and if we take $A=B=C=60^{~\text{o}}$ then $x=1$($ABC$ is a Equilateral).
Now take $A=90^{~\text{o}},B=45^{~\text{o}},C=45^{~\text{o}}$ and using  $b=a\sin(B), c=a\cos(B)$ we have: $$x=\frac{a^2\sin(B)+a^2\sin(B)\cos(B)+a^2\cos(B)}{a^2}\sim 0.9$$ It seems that $x\leq1$.
