1. **Problem Statement:** Determine the value of load resistor $R_L$ for maximum power transfer in a circuit with a voltage source $V_S = 42$ V and a series resistor $R_1 = 21$ Ohm. 2. **Formula and Rule:** The Maximum Power Transfer Theorem states that maximum power is delivered to the load when the load resistance equals the Thevenin resistance seen from the load terminals. Mathematically, for maximum power transfer: $$R_L = R_{Thevenin}$$ 3. **Applying the Rule:** Since $R_1$ is the only resistor in series with the voltage source, the Thevenin resistance seen by the load $R_L$ is simply: $$R_{Thevenin} = R_1 = 21 \text{ Ohm}$$ 4. **Conclusion:** Therefore, the appropriate value of $R_L$ for maximum power transfer is: $$R_L = 21.00 \text{ Ohm}$$ This value is already precise to two decimal points as requested.