$T \propto(\Delta \ell)$

$T = k (\Delta \ell)$

Let, $\ell_{0}=$ natural length (original length)

$\Rightarrow T = k \left(\ell-\ell_{0}\right)$

so, $T _{1}= k \left(\ell_{1}-\ell_{0}\right)$ And $T _{2}= k \left(\ell_{2}-\ell_{0}\right)$

$\Rightarrow \frac{ T _{1}}{ T _{2}}=\frac{\ell_{1}-\ell_{0}}{\ell_{2}-\ell_{0}}$

$\Rightarrow \ell_{0}=\frac{ T _{2} \ell_{1}- T _{1} \ell_{2}}{ T _{2}- T _{1}}$