Ask Me Help Desk - Do I use the P=2l+2w with another formula

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Do I use the P=2l+2w with another formula

An indoor physical-fitness room consists of a rectangular region with a semicircle on each end . The perimeter of the room is to be a 200-meter running track. What measurements will produce a maximum area of the rectangle?

Do you have any other dimensions you forgot? Just checking.

The perimeter is $P=2{\pi}r+2y=200; \;\ {\pi}r+y=100$

The area is $A=2ry+{\pi}r^{2}$

You could solve P for y and sub into A, then differentiate, set to 0 and solve for r.

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