Maximum power transfer in a circuit

[gfd43tg]

Homework Statement

a) What value of the load resistor RL will extract the maximum amount of power from the circuit below?
b) How much power will that be?
Hint: you need to use both the concepts of Thevenin equivalent circuits and maximum power transfer.

Homework Equations

The Attempt at a Solution

I am confused why the ''source voltage'' is the thevenin voltage and not the actual source, or why I have to solve this problem with a thevenin equivalent? Also, is the method correct and did I solve it correctly?

 

[rude man]

100% correct.

You didn't have to solve it using thevenin but it's a good way to do it.
You never have to use thevenin or norton unless the prof insists on it. But again it's often good to do so, as in this case. The alternative is 3 equations in 3 unknknowns with some pretty horrible expressions. With thevenin you're taking advantage of the fact that max power happens when the load R = source R, for a given source R.