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jbmow
Since a square is a rectangle, each side of the square is 50 and its area would be 2500 ft^2.  A square of a quadrilateral yields the largest area.
Cetacea

Dimensions are 50 feet by 50 feet.

Let the length = x

the width = y

So the perimeter = 2(x+y)=200

or, x+y=100

or, y=100-x

So the area is = A = xy = x(100-x).

For greatest area A' = 0 and A" < 0.

[tex]A= x(100-x)\\A=100x-x^2\\A'=100-2x\\A''=-2[/tex]

We set A'=0 to find x.

[tex]100-2x=0\\2x=100\\x=50[/tex]

For x=50, A"=2 < 0

It means for x=50, y=100-50=50 the rectangle will have the greatest area.

Learn more: https://brainly.com/question/14324158

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