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Minimizing the Perimeter of a Sector with Given Area

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

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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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 Roberta Grech
"Minimizing the Perimeter of a Sector with Given Area"
 http://demonstrations.wolfram.com/MinimizingThePerimeterOfASectorWithGivenArea/
 Wolfram Demonstrations Project
 Published: November 22, 2010
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Related Curriculum Standards

US Common Core State Standards, Mathematics