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max of S/(2S+p+2), S,p area, perimeter of a rectangle fixed S (HOMC 2013 J Q10 )

Source:

July 28, 2019

geometryperimeterrectangle

Problem Statement

Consider the set of all rectangles with a given area

S

. Find the largest value o

M = \frac{S}{2S+p + 2}

where

p

is the perimeter of the rectangle.