Simon has 160 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width www (in meters) is modeled by a(w)=-w(w-80) what is the maximum area possible?

It is given in the question , that Simon has 160 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width w (in meters) is modeled by [tex] A(w) = -w(w-80) \\ A(w) = -w^2 + 80w [/tex]Which represents parabola and the parabola is maximum at its vertex, that is[tex] w = -\frac{b}{2a} = - \frac{80}{2} = 40 meters [/tex]Therefore the width is 40 meters and the area is[tex] A(40) = -40(40-80) = -40*-40 = 1600 meter ^2 [/tex]