NEED HELP ASAP AS SOON AS POSSIBLE, WILL GIVE 69 POINTS A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.

The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.

Jovana was trying to find a formula for that perimeter with one side 8 yards longer than the other side using the area. In which step did she make a mistake?

Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Explain her mistake. What is the correct formula?

Mark Brainliest please

Explanation

Jovana needs to solve the equation x(x+8) = 256 for x

To do so, first distribute and get everything to one side

x*(x+8) = 256
x*x+x*8 = 256
x^2+8x = 256
x^2+8x-256 = 0

Now use the quadratic formula (a = 1, b = 8, c = -256)

x=−b±b2−4ac/√2a

x=−(8)±82−4(1)(−256)/√2(1)

x=−8±1088/√2

x≈−8±32.98485/2

x≈−8+32.98485/2 or x≈−8−32.98485/2

x≈24.98485/2 or x≈−40.98483/2

x≈12.49242 or x≈−20.49242

Another approach is to graph x^2+8x-256 and locate the roots as shown below
wwwdotdesmosdotcom/calculator/0miqroxamw
which leads to the same approximate solutions

Ignore the negative solution because a negative length or width makes no sense.

So the only practical x value is roughly 12.49242

If x = 12.49242, then
x+8 = 12.49242+8 = 20.49242

Therefore
Width = W = 12.49242
Length = L = 20.49242
which are approximate

The perimeter is approximately
P = 2*(L+W)
P = 2*(20.49242+12.49242)
P = 65.96968

Side Note:
A = L*W = 20.49242*12.49242 = 255.9999174564
which is fairly close to 256