SOLUTION: Using 36 feet of rope, enclose a rectangle with the largest possible area. Enclose a rectangle with the smallest possible area. In both cases use dimensions that are whole feet.
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Question 437678: Using 36 feet of rope, enclose a rectangle with the largest possible area. Enclose a rectangle with the smallest possible area. In both cases use dimensions that are whole feet. Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! The largest possible area occurs when the figure is a square (it is possible to prove this using the vertex of a parabola, or by calculus, or by AM-GM inequality). If it is a square, the side length would be 9 ft, and the area is 81 ft.
The smallest possible area is about zero. This occurs when the length approaches zero and the width approaches 18. In rigorous terms, if L, 18-L are the length and width, then
