idnof
Apr 4, 2008, 08:34 AM
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?
galactus
Apr 4, 2008, 03:34 PM
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.