10

Part of 2013 Hanoi Open Mathematics Competitions

Problems(2)

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

Source:

Consider the set of all rectangles with a given area

S

. Find the largest value o

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

p

is the perimeter of the rectangle.

geometryperimeterrectangle

max of (16-p)/(p^2+2p), S,p area, perimeter, fixed s (HOMC 2013 Q10)

Source:

Consider the set of all rectangles with a given area

S

. Find the largest value o

M = \frac{16-p}{p^2+2p}

p

is the perimeter of the rectangle.

geometryperimetermaximumarea