Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeterpis a square.

Let the sides of the rectangle bexandyand letfandgrepresent the area (A) and perimeter (p), respectively. Find the following.

A=f(x,y)=xy

p=g(x,y)=2x+2y

f(x,y)=?

g=?

Then=1

2

y=?

implies thatx=?.

Therefore, the rectangle with maximum area is a square with side length.