To find the equivalent wire that has the same resistance between points \(X\) and \(Z\), we need to analyze the given setup and calculate the total resistance.

The three wires in the setup are arranged in such a way that two wires, each with resistance \(R\), are in parallel, and this combination is in series with another wire of resistance \(R\).

Step-by-step Calculation:

1. Calculate the resistance of each wire:
   • The resistance of a wire is given by the formula: \(R = \frac{\rho L}{A}\).
   • For each wire, \(R = \frac{\rho L}{A}\).
2. Calculate the equivalent resistance of the two parallel resistors:
   • The formula for two resistors, \(R\) in parallel is: \(\frac{1}{R_{\text{parallel}}} = \frac{1}{R} + \frac{1}{R}\).
   • Thus, \(R_{\text{parallel}} = \frac{R}{2} = \frac{\rho L}{2A}\).
3. Calculate the overall series resistance:
   • Add the series resistance: \(R_{\text{total}} = R_{\text{parallel}} + R\).
   • Substituting values: \(R_{\text{total}} = \frac{\rho L}{2A} + \frac{\rho L}{A} = \frac{3\rho L}{2A}\).
4. For the equivalent single wire with resistance \(R_{\text{new}}\), we have:
   • \(R_{\text{new}} = \frac{\rho L_1}{A_1}\) should equal \(R_{\text{total}} = \frac{3\rho L}{2A}\).
   • Equating the resistances: \(\frac{\rho L_1}{A_1} = \frac{3\rho L}{2A}\).
   • This simplifies to: \(\frac{L_1}{A_1} = \frac{3L}{2A}\).
   • One possibility is \(L_1 = 3L\) and \(A_1 = 2A\).

Conclusion:

Thus, the correct option is:

\(L_1 = 3L\) and \(A_1 = 2A\)