College math/bus calc

A rectangular-shaped garden has one side along the side of a house. the other three sides are to be enclosed with 60ft of fencing. what is the largest possible area of such a garden?

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  1. x = length
    y = width
    A = x y
    P = 60 = x + 2 y
    so
    x = 60 - 2 y

    A = (60 - 2 y) y = 60 y - 2 y^2

    2 y^2 - 60 y = -A
    y^2 - 30 y = -A/2
    complete square for vertex of parabola
    y^2 - 30 y + 225 = -A/2 + 225
    (y-15)^2 = -A/2 + 225 = -(1/2)(A-450)
    so y = 15 at vertex
    A = 450 at vertex
    so
    15 by 30 for 450 ft^2 area

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