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?
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.