Find the dimensions of a rectangle with area 1600 m^2 whose perimeter is as small as possible.

Answer 1

LW = 1600 So, W = 1600/L

P = perimeter = 2L + 2W = 2L + 3200/L

P' = 2 - 3200/L² = (2L² - 3200) / L²

P' = 0 when 2L² = 3200

L² = 1600

So, L= 40 and W = 40

Answer 2

(L)(W) = 1600

W = 800 - L

L(800 - L) = 1600

Choice:

Put into vertex form and determine minimum

Take first derivative, set to zero, and solve