Question

You have 300 feet of fence. You need to build a garden, where 3 walls are fence and the 4th wall is your house. What is the maximum area of the garden you can make with 300 feet of fence?

Answer 1

let the single side be y ft, the two equal sides be x
2x + y = 300
y = 300-2x

area = xy = x(300-x)
= -2x^2 + 300x

you want the vertex of this downwards parabola
the x of the vertex is -b/(2a) = -300/-4 = 75
y = 300-150 = 150
max area = xy = 75(150) = 11250 ft^2