SOLUTION: Here's another word problem I'm having trouble with. Again, I feel like I know how to do this but I can't get the right equation to start with. If nothing else could you please hel

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Question 248947: Here's another word problem I'm having trouble with. Again, I feel like I know how to do this but I can't get the right equation to start with. If nothing else could you please help me get the right equation. I would greatly appreciate it!
Problem: A window consists of an open rectangle topped by a semicircle and is to have a perimeter of 288 inches. Find the radius of the semicircle that will maximize the area of the window.
I drew a picture and labeled it the best I could. I wrote down that the perimeter of a circle is 2%2Api%2Ar I also wrote that the perimeter of a rectangle is 2l%2B2w but that's about all that I could do. Please help! Thank you in advance for your help.
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
If this isn't a calculus problem then we need to use the fact that a square maximizes the area for a rectangle with a given perimeter. Let's say the half circle at the top is R. Then each side of the square is 2*R.
The perimeter of the semi-circle is half the circumference so that is 1/2(2*pi*R) which is then pi*R.
So the entire perimeter is given by:
pi*R + 3*(2*R)= 388.
Now you can solve for R.