The diagram shows a sporting track made up of a rectangle with semicircles at each end. The

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The diagram shows a sporting track made up of a rectangle with semicircles at each end.


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The rectangle has dimensions p meters by 2r meters where r is the radius of each semicircle. The perimeter of the track is 1400 m. The track has a maximum area for this perimeter. Find the value of p and the value of r.

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