Suppose that you have 760 feet of rope and want to use it to make a rectangle. What dimensions should you make your rectangle if you want to enclose the maximum possible area?

Answer 1

760/4 = 190 feet for each side, to maxize area

max area = 190^2 = 36,100 ft^2

a square gives the largest area for a fixed perimenter

or use calculus

A= Lw

2(L+w) = 760

L = 380-w

A= (380-w)w

A =380w-w^2

A'=380-2w = 0

2w =380

w =380/2 = 190 feet wide

L= 380-190 = 190 feet long