Assuming Hooke's law to be valid. $$ \begin{aligned} & \mathrm{T} \propto(\Delta \ell) \\ & \mathrm{T}=\mathrm{k}(\Delta \ell) \end{aligned} $$ Let $\ell_0=$ natural length (original length) $$ \begin{aligned} & \Rightarrow \mathrm{T}=\mathrm{K}\left(\ell-\ell_0\right) \\ & \text { so, } \mathrm{T}_1=\mathrm{k}\left(\ell_1-\ell_0\right) \& \mathrm{~T}_2=\mathrm{k}\left(\ell_2-\ell_0\right) \\ & \Rightarrow \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\ell_1-\ell_0}{\ell_2-\ell_0} \\ & \Rightarrow \ell_0=\frac{\mathrm{T}_2 \ell_1-\mathrm{T}_1 \ell_2}{\mathrm{~T}_2-\mathrm{T}_1} \end{aligned} $$