We know that, R = rho * L / A

So we need the resistance to be constant, Therefore, rho * L / A = constant

or, L directly proportional to (A / rho)

Now the material of the resistance should also be should also be the same, Hence, we get, L is directly proportional to A

So to double the length of the resistance without changing the resistance its area of cross section must also be doubled. This means that the volume of the resistor would increase so we need to add more material to the resistor.

But if the area of cross section also remains constant then check out the next answer.

We know that, $\displaystyle R = \rho \,\frac{L}{A}$.

So we need the resistance to be constant, Therefore, $\rho\dfrac{L}{A} = \text{constant}$

or, $L\propto \dfrac{A}{\rho}$.

Now the material of the resistance should also be should also be the same, Hence, we get, $L \propto A$.

So to double the length of the resistance without changing the resistance its area of cross section must also be doubled. This means that the volume of the resistor would increase so we need to add more material to the resistor.

But if the area of cross section also remains constant then check out the next answer.