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Answer:
Perimeter of rectangle states that total distance around the outside, which can be found by adding together the length of each side.
As per the given statement, Dana has 800 yards of fencing to enclose a rectangular area.
Therefore, perimeter of rectangle = 800 yards.
Perimeter(P) of rectangle is given by :
P = 2(x+y) where x is the length and y is the width of the rectangles respectively.
Then,
2(x+y) = 800
Divide both sides by 2 we get;
x+y =400
or
y = 400 -x .....[1]
We know, the area(A) of rectangle is given by
A = xy .....[2]
Substitute equation [1] into [2] we get;l
A = x(400-x)
using distributive property
or
......[3]
To maximize the enclosed area.
For a quadratic function in standard form , the axis of symmetry is a vertical line given by;
Then; we have from equation [3]
a = -1 and b = 400
By axis of symmetry;
=
Substitute in equation [1] to solve for y:
y = 400 - 200 = 200
The dimensions of the rectangle that maximize enclosed area are:
x = 200 units and y = 200 units.
Maximum area = square units.
We can say that maximum area of rectangle will always be a square