The resistance #R# of the wire depends on two factors - its geometry and its material property,
#R = \rho L/A#, where #\rho# is the resistivity which is a material property. The other two are geometrical parameters. #L# is the length and #A# is the cross-sectional area.
When a wire is stretched, its length increases while its cross-sectional area decreases accordingly to keep the volume a constant.
Volume: #\quad V = L_1A_1 = L_2A_2;#
#A_2/A_1 = L_1/L_2# ...... (1)
#R_1=\rhoL_1/A_1;\qquad R_2=\rhoL_2/A_2#
#R_1/R_2 = (L_1/L_2)(A_2/A_1) = (L_1/L_2)^2 = (1/3)^2 = 1/9#
#R_2 = 9R_1#
