Right well lets first find perimeters.
for the rectangle its .
So for the square it's just whatever is left which is .
So area of the rectangle is width times length which is .
Each side of the square has length .
Hence area of the square is...
Hence total area is...
To find the minimum find the derivative and set it to be 0.
To show it is a minimum find the second derivative and check if it is greater than 0.
EDIT: I see Soroban is replying to this thread as well. He will explain this better if you are still confused.