SOLUTION: Please help me solve this problem: A rope 18 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing

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Question 616579: Please help me solve this problem:
A rope 18 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing the area of both square and circle as a function of the length of one side of the square.
I can get to A(s)= pi(9-2s/pi)^2+s^2 but I am lost after that.
Found 2 solutions by solver91311, richwmiller:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You could take what you have and manipulate it until you end up with something that looks like:

But I don't see much advantage to my representation over the one you have. Possibly easier to take the derivative of mine, but probably not worth the effort.

I would just leave it the way you have it and call it good.

John

My calculator said it, I believe it, that settles it

Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
c+s=18
c= circumference of circle
s= perimeter of square
c=18-s
Area of square=(s/4)^2
2*pi*r=c
r=c/(2*pi)
Area of circle=pi*r^2=
Area of circle=pi*(c/(2*pi))^2
Area of circle=pi*((18-s)/(2*pi))^2
Area of circle=(18-s)^2/(4 pi)