Calculating the output power from an Amplifier
Here, power gain given is for the amplifier, not for the entire circuit. So you have to find the power at the amplifier input first. Then multiply by G.

The current \$i_1\$ is split equally across \$R_1\$ and \$R_2\$. Therefore current to the input of amplifier (flowing through \$R_2\$) is \$i_1/2\$. Therefore power transferred from source to amplifier input is \$(i_1/2)^2\times R_2 = i_1^2R_2/4 = i_1^2R_1/4\$. 



OR

Max power transfer theorem also says that when the loads are matched, the power transferred is \$I_{rms}^2R_L/4\$. Here source is \$i_1\$ (with \$R_1\$ in parallel) and load is amplifier (input). Hence the answer.