Answer:
9R
Explanation:
We know that the resistance is [tex]R=\rho *\frac{L}{A}[/tex].
If we stretch the wire to a new length L2 = 3L, the cross-sectional area will also change. If the cross-sectional area doesn't change throughout the wire, we can say that:
Volume = L*A = 3L * A2 being A2 the new area after stretching the wire.
Since the volume remains the same we conclude that A2 = A/3
With this information, we calculate the new resistance:
[tex]R2=\rho *\frac{L2}{A2}=\rho *\frac{3*L}{A/3}=\rho * 9 * \frac{L}{A}[/tex]
Since [tex]R=\rho *\frac{L}{A}[/tex], and by simple inspection of the previous equation, we get:
R2 = 9*R
