Minimum perimeter rectangles Of all rectangles with a fixed area A, which one has the minimum perimeter? (Give the dimensions in terms of ?A.?)

Solution Step 1: Solution Step 1: Consider a rectangle of width x and length y here area of rectangle(length *width) is a constraints denote it by A Thus the constraints A=xy And perimeter of a rectangle is the objective function that is P=2(x+y) Our goal is to find the dimension of a rectangle in terms of A which gives minimum perimeter Step 2: The first step is to use the constraints to express the objective function P=2(x+y) in terms of a single variable For this A=xy A y = x Step 3: Substitute for y the objective function p becomes p=2(x+y) A =2(x+ )x P=2x+ 2A x Which is the function of single variable with x