Why would one need to know the radiation resistance of an antenna?

Knowing the radiation resistance is essential for designing feed systems because it forms the primary part of an antenna's feed-point impedance (along with ohmic losses and any reactance). According to the maximum power transfer theorem, a transmitter delivers maximum power when the load impedance perfectly matches the source impedance (typically 50 ohms). If the radiation resistance results in an unmatched impedance, matching networks or transformers must be used. Options relating to near-field radiation density, front-to-back ratio, or front-to-side ratio are incorrect because those depend on the antenna's directional pattern, not its feed-point resistance.