# SOLUTION: The length and width of a rectangle have a sum of 78.

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 Geometry: Rectangles Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Rectangles Question 426590: The length and width of a rectangle have a sum of 78. Answer by ewatrrr(10682)   (Show Source): You can put this solution on YOUR website! ``` 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. ```