Let L and W represent the length and width respectively
L + W = 78 or W = (78-L)
What dimensions give the maximum area?
area = L(78-L) = - L^2 + 78L
Completing the square to find the vertex: parabola opens downward, vertex is max PT
Area= -[(L-29)^ - 29^2] = -(L-29)^2 + 29 Maximum Pt (29, 29^2)
L = 29 gives the maximum area, width is also 29 (78-39)
Square with side 29 has the maximum area.