Rich G. answered • 09/18/18

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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 - 2W

^{2}If we rearrange this equation we get

2W

^{2}-360W + A = 0Now 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.