SOLUTION: What is the maximum area of a rectangle given that its perimeter is 32 feet? Choices... 32ft, 128ft, 256ft, or 64ft. I tried 12 by 4 but i did not work. And I tried 15 by 2. I

Algebra ->  Rectangles -> SOLUTION: What is the maximum area of a rectangle given that its perimeter is 32 feet? Choices... 32ft, 128ft, 256ft, or 64ft. I tried 12 by 4 but i did not work. And I tried 15 by 2. I       Log On


   

Question 321510: What is the maximum area of a rectangle given that its perimeter is 32 feet?
Choices... 32ft, 128ft, 256ft, or 64ft.
I tried 12 by 4 but i did not work. And I tried 15 by 2. I dont know any other ways to solve for this question.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
2L + 2W = 32 ___ L + W = 16 ___ L = 16 - W

A = L * W = (16 - W)W = 16W - W^2 ___ this is a downward opening parabola with the maximum for A at the vertex
___ the vertex is on the axis of symmetry

W = -b / 2a = -16 / [2*(-1)] = 8

A = (16 - 8)8 = 64

the rectangle with the maximum area is a square