Minimizing the Perimeter of a Sector with Given Area

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Given the area of a sector, find the value of the radius that minimizes the perimeter of the sector with that area.

Contributed by: Roberta Grech (November 2010)
Open content licensed under CC BY-NC-SA


This is a typical minimization problem encountered by calculus students as an application of differentiation.

The Demonstration is based on Problem 26 in C. Gauci and K. Asciak, Intermediate Pure Mathematics, 3rd ed., Malta: Progress Press, 2005 p. 154.


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