For ensuring dissipation of same energy in all t h r e e resistors...

As the voltage in $R_2$ and $R_3$ is same therefore, according to, H=$\frac{V^2}{R} \cdot$t, \quad R_2=R_3 Also the energy in all resistance is same. \therefore \quad i² R_1 t=i_1^2 R_2 t $<img src="/api/proxy-image?url=https$ \\ $\mathrm{U} \operatorname{sing} \quad \dot{h}_1=\frac{R_3}{R_2+R_3} i=\frac{R_3}{R_3+R_3} i=\frac{1}{2} i$ Thus $i^2 R_1 t=\frac{i^2}{4} R_2 t \quad$ or, $R_1=\frac{R_2}{4}$.