samiz6904 samiz6904
  • 12-11-2017
  • Mathematics
contestada

Find the smallest perimeter and the dimensions for a rectangle with an area of 225 in^2

Respuesta :

shinmin
shinmin shinmin
  • 22-11-2017

To solve this, let the dimensions be x and y. We know that the area is 225. So, x * y = 225 


Let the perimeter be denoted as P.


P = 2x + 2y 


sine y = 225/x 


P = 2x + 450/x 


P' = 2 - 450/x^2 


P'' = + 900/x^3 


Put P' = 0 


then x = 15 


at x =15 P'' is positive 


So the minimum perimeter, will be:
P = 2 (15 + 15) = 60 cm

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