#### Answer

a. 1.7 T.
b. 0.58.

#### Work Step by Step

The stars behave like blackbodies and obey the Stefan-Boltzmann law, and Wien’s displacement law.
The Stefan-Boltzmann law says that the intensity of the radiation is proportional to the fourth power of the absolute temperature, so the total radiated power is $P=\sigma A T^4$.
a. The hot and cool stars each radiate the same total power, so the Stefan-Boltzmann law gives this:
$$\sigma A_c T_c^4=\sigma A_h T_h^4$$
The cooler star has 3 times the radius of the hotter star.
$$\sigma 4 \pi(3R_h)^2 T_c^4=\sigma 4 \pi (R_h)^2 T_c^4$$
$$9 T_c^4=T_h^4$$
$$T_h=1.7 T_c$$
We rounded $\sqrt{3}$ to 2 significant figures.
b. Using Wien’s law, take the ratio of the peak wavelengths.
$$\frac{\lambda_{m,hot}}{\lambda_{m,cool}}=\frac{T_c}{T_h}=\frac{1}{\sqrt{3}}=0.58$$