Brett wants to use 40 feet of twine to mark off a rectangular area in his yard for a garden. What are the length and width for a garden with the greatest area?

Answer 1

or, less aggressively,

if the garden is x by y feet,

2x+2y=40
x+y=20
y=20-x

area a = xy = x(20-x)

a parabola reaches its vertex halfway between the roots. So, at x=10 we have max area.

The garden is a 10x10 square.