Jim wants to build a rectangular parking lot along a busy street but only has 2,700 feet of fencing available. If no fencing is required along the​ street, find the maximum area of the parking lot.

I got the answer 911.25 which was incorrect I'm not sure what im doing wrong

f(x)=3x^2+3x-3 if f(-x)=

To find the maximum area of the parking lot given the amount of fencing available, we can use the concept of optimization. Let's break down the problem step-by-step:

1. Let's assume the length of the rectangular parking lot is L, and the width is W.
2. Since no fencing is required along the street, we can consider that the length L is divided into two parts, one for the front and one for the back. The width W will be the same on both sides.
3. Taking into account the fencing required for this rectangular shape, we have 2(L/2) + 2W = 2700 feet.
This simplifies to L + 2W = 2700.
4. We need to isolate one of the variables, either L or W, in terms of the other.
Let's isolate L: L = 2700 - 2W.
5. Now we have the area of the parking lot, A = L * W.
Substituting the value of L from step 4 into this equation, we get A = (2700 - 2W) * W.
6. Expanding the equation, we have A = 2700W - 2W^2.
7. To find the maximum area, we differentiate the equation with respect to W and set it equal to zero:
dA/dW = 2700 - 4W = 0.
Solving this equation, we find W = 675 feet.
8. Plugging this value of W back into L = 2700 - 2W, we get L = 1350 feet.
9. Finally, substitute these values of L and W into the equation for the maximum area:
A = L * W = 1350 * 675 = 911,250 square feet.

So, the maximum area of the rectangular parking lot with 2,700 feet of fencing available is 911,250 square feet. It seems that you made an error in calculating the final area, which led to the incorrect answer.

To solve this problem, you need to determine the dimensions of the rectangular parking lot that will result in the maximum possible area, given the available fencing.

Let's assume the width of the parking lot is "w" and the length is "L". We are told that there is no fencing required along the street, so the length will be perpendicular to the street.

According to the given information, the total amount of fencing available is 2,700 feet. Since no fencing is required on one side (the street side), we have three sides to consider - two equal sides of length "w" and one length side of length "L". This can be represented as:

2w + L = 2700

Now, we need to express either "w" or "L" in terms of the other variable to solve for the maximum possible area.

Let's solve for "w" in terms of "L" by rearranging the equation:

2w = 2700 - L
w = (2700 - L)/2

The area of the rectangle is given by the product of the width and length:

Area = w * L = [(2700 - L)/2] * L

To find the maximum area, we need to differentiate this expression with respect to "L" and set it equal to zero, then solve for "L".

d(Area)/dL = (2700 - 2L)/2 - 0 = 0
2700 - 2L = 0
2L = 2700
L = 2700/2
L = 1350

Now that we have the value for "L", we can substitute it back into the equation to find the corresponding value for "w":

w = (2700 - L)/2
w = (2700 - 1350)/2
w = 1350/2
w = 675

So, the dimensions of the rectangle that will result in the maximum possible area are a length of 1350 feet and a width of 675 feet. To find the maximum area, we can use the formula:

Area = Length * Width
Area = 1350 * 675
Area = 911,250 square feet

Therefore, the correct maximum area of the parking lot is 911,250 square feet, not 911.25.

w: width of the parking

ℓ: length of the parking

The perimeter of the parking is the length of the fence:

2.(ℓ + w) = 2700

ℓ + w = 2700/2

w = 2700/2 - ℓ

The area of the parking is:

a = w * ℓ → you know that: w = 2700/2 - ℓ

a = (2700/2 - ℓ).ℓ

a = 2700/2ℓ - ℓ² ← this is a function of ℓ