# 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

## Details

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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