# Thread: optimization: maximize area of rectangle inside track

1. ## optimization: maximize area of rectangle inside track

I have this problem i cannot figure out. It uses optimization:

There is a rectangular field with a semicircle on each end and a track around the whole thing. The perimeter of the inner edge of the track is 1256 meters.

I need to maximize the area of the rectangle. How do I do this?

2. You know the perimeter of the track:

$\L\\1256=2x+2{\pi}r$...[1]

The area of the rectangle is:

$\L\\2rx$...[2]

Solve [1] for x, sub into [2], differentiate, set to 0 and solve for r.

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