The length of a metal wire is  $l_1$ when the tension in it is $T_1\&l_2$  when the tension is $T_2$ .  The natural length of the wire is

Let $l_0$  be the natural length of wire and A be the cross-sectional area. 
Using Hooke’s law,
 $\sigma \left(\text{stree}\right)\infty \in \left(\text{strain}\right)$
 $\Rightarrow \frac{{\sigma }_1}{{\sigma }_2}=\frac{{\in }_1}{{\in }_2}$
 $\Rightarrow \frac{T_1/A}{T_2/A}=\frac{(l_1-l_0)/l_0}{(l_2-l_0)/l_0}$
 $\Rightarrow \frac{T_1}{T_2}=\frac{l_1-l_0}{l_2-l_0}$