I have to calculate the resistance of the adjustable resistor whenthepower delivered to the 5 ohm resistor is 40W.

Im just not sure where to begin, i know the voltage will be the same for the resisters in parallel but im not sure how to work out that voltage because im missing the variable resistance. And thus im not sure how to work out the current. Iv been looking at all of the equation triangles and cant find any that will help me, i think im just not sure what.

 

For the 5 ohm resistor to dissipate 40W, the voltage across it equals:

V=sqrt(P*R)=sqrt(40*5)=14.14V

This is the same voltage across the 20 ohm resistor.

I will leave you do the rest.