Explanation
the electrical resistivity is define as
[tex]\begin{gathered} \sigma=R\frac{A}{l} \\ where \\ R\text{ is the electrical resitance} \\ \text{A is the cross seccional area} \\ l\text{ is the length} \end{gathered}[/tex]so,if we isolate R
[tex]\begin{gathered} \sigma= R\frac{A}{l} \\ R=\sigma\frac{l}{A} \end{gathered}[/tex]hence, the ratio of the resitances is
[tex]\frac{R_1}{R_2}=\frac{\sigma\frac{l}{A}}{\sigma\frac{l_2}{A}}[/tex]the volume of the wire is constant , therefore
[tex]A_1l_1=A_2l_2[/tex]if the new length is twice the original