Hi

Let L and W represent the length and width respectively

Question states***

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.

    

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