240 m of fencing material is going to be used to enclose three sides of a rectangular lot. What should the

dimensions of the lot be so that the enclosed area is as large as possible? (I'm supposed to solve this using a quadratic equations but I don't know how...)

area=lenght*width

240=length+2widdth
or length=240-2W

area=(240-2w)w
So where are the zeroes? at w=0, and w=120.

Where is the maximum? halfway between the zeroes, or at 60=width

To solve this problem, we can start by understanding the constraints given. The problem states that we have 240 m of fencing material to enclose three sides of a rectangular lot. This means that one side of the rectangular lot will already have a boundary, so we only need to find the dimensions for the other two sides.

Let's assume the length of the rectangular lot is 'L' and the width is 'W'. Since we only have to enclose three sides, the perimeter of the rectangular lot will be:

Perimeter = Length + 2 * Width

Since we are given that the total amount of fencing material is 240 m, we can write the equation as:

240 = L + 2W

To maximize the enclosed area, we need to come up with a quadratic equation. The area of a rectangular lot is given by:

Area = Length * Width

Now we can substitute the value of Length from the first equation into the area equation:

Area = (240 - 2W) * W

Expanding the equation, we have:

Area = 240W - 2W^2

To maximize the area, let's find the vertex of this quadratic equation. The vertex can be found using the formula:

W = -b / (2a)

In our equation, a = -2 and b = 240, so substituting these values into the formula:

W = -(240) / (2 * -2)
W = 120

So, the value of W that maximizes the area is 120. We can substitute this value back into the equation to find the length (L):

240 = L + 2(120)
240 = L + 240
L = 240 - 240
L = 0

Therefore, the dimensions of the lot that would maximize the enclosed area are:
Length = 0 m
Width = 120 m

Note: Since Length = 0 m, this implies that the three sides being enclosed will be two equal sides of length 120 m and one side of length 0 m.