Rich G. answered 09/18/18
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Adjunct instructor tutoring middle school through college
The area is based on the length and width of the fenced area, which depends on the fencing material he has.
Since he only has to fence 3 sides of the field, the perimeter of the field is width + length + width, or P = 2W + L
We know that the perimeter will equal 360 meters, so:
360 = 2W + L
or
360 - 2W = L
The area of a rectangle is width * length, or A = W*L
Since L = 360 - 2W we can rewrite our area equation as
A = W (360-2W)
If we multiply this out we get
A = 360W - 2W2
If we rearrange this equation we get
2W2 -360W + A = 0
Now we have a quadratic equation. The max/min of a quadratic is at the vertex. To find the x axis point of the vertex we use the equation
X = -b/2a
Which in this case will be the width of the field.
Width = -(-360)/2(2) = 360/4 = 90
So our width at the maximum area will be 90 meters. You can use the other equations to find the length and area of the field from there.