Ahomeowner has 208208 feet of fence to enclose a rectangular garden. what dimensions would yield the maximum area for the garden? what is the maximum area of the garden? length (ft)equals=104104 width (ft)equals=104104 the maximum area is (sq. ft)equals=nothing.

Step-by-step explanation:

Maximum area is enclosed by a polygon when that polygon is regular. A regular 4-sided polygon is a square. The side length of a square is 1/4 of the perimeter, so for a perimeter of 208 feet, the side length is 52 feet.

The dimensions of the maximum-area garden are 52 feet by 52 feet. The area of that is (52 ft)² = 2704 ft².

You can go at this using calculus, but that is not necessary. It is sufficient to observe that the sum of two adjacent sides of a rectangle of perimeter 208 feet will be 104 feet. So, for length x, the width will be 104-x and the area is ...

  area = x(104 -x)

This quadratic function graphs as a parabola opening downward. It has x-intercepts of x=0 and x=104. Its vertex (maximum) is located on the line of symmetry at x = 52.

because they could drop even lower..

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