maximizing perimeter of rectangle under sine

Due to symmetry of sine wave, x+w+x = Pi/2, width = Pi/2-2x.

We alreay know the length 3sin(2x), now find the max perimeter, what is the problem?
 
The original problem asked us to solve for "k" when the perimeter of the rectangle is a maximum and 2k is equal to the length of the rectangle.
 
Well, we are all in agreement on the answer, the only problem now is that the answer key has a different answer (not a problem for the forum exactly). I have contacted the writer about the issue. Thanks everyone for all your help in assisting me to understand this problem. I appreciate your time! :D
 
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