Perimeter = 300
Area = a(w)
Width = w
Perimeter = 300 and width = w ⇒ length = [300 - 2w ]/2 = 150 - w
Area, A = width * length = w(150-w) = 150w -w^2
Roots = w = 0 and w =150
Vertex
w =[0 + 150]/2 = 75
A = 75(150-75) = 75^2 = 5625
(75,5625)
Given that the coefficient of w^2 is negative, the vertex is the maximum of the function or area.
The second coordinate of the vertex (5625) is the maximum area the fence can enclose.
Answer: the maximum area that can be enclosed by the fencing.
Hope this helps!
