A gardener wants to fence in her plot in two equal rectangular sections. If she has 120 yards of fence and the area of the entire plot is 384 yd 2, find the possible dimensions in yards of the garden.

Eq1: L*W = 384yds^2.

@l + 2W = 120
Divide both sides by 2:
L + W = 60.

Eq1: L * W = 384.
Eq2: L + W = 60.
Solve for L in Eq2:
L = 60 - W.
In Eq1, substitute 60-W for L:
(60-W)W = 384
-W^2 + 60W -384 = 0.
Solve using Quadratic Formula and get:
W = 7.28 or 52.7.
Substitute 7.28 for W in Eq1:
7.28*L = 384
L = 52.7 Yds.

Solution:
L = 52.7 Yds.
W = 7.28 Yds.

To form 2 equal rectangular sections:
L = 52.7 Yds.
W = 7.28/2 = 3.64 Yds.
OR
L = 52.7 / 2 = 26.35 Yds.
W = 7.28 Yds.

To solve this problem, we need to set up equations based on the given information.

Let's assume the dimensions of each rectangular section as follows:
Length of section 1 = L1
Width of section 1 = W1
Length of section 2 = L2
Width of section 2 = W2

We have two equations based on the perimeter and area of the entire plot:

Perimeter equation:
2L1 + 2W1 + 2L2 + 2W2 = 120

Area equation:
L1 * W1 + L2 * W2 = 384

Since the gardener wants to divide the plot into two equal sections, the dimensions of the two sections should be the same.

Therefore, we can set L1 = L2 = L and W1 = W2 = W.

Substituting these values into the equations, we get:

2L + 2W + 2L + 2W = 120
4L + 4W = 120

Simplifying the equation further, we have:
L + W = 30

And for the area equation, we get:
L * W + L * W = 384
2LW = 384

Now, we have a system of equations to solve:
L + W = 30
2LW = 384

Solving the first equation for either L or W, we get:
L = 30 - W

Substituting this value into the second equation, we get:
2(30 - W)W = 384

Expanding and simplifying, we have:
60W - 2W² = 384

Rearranging the equation, we get a quadratic equation:
2W² - 60W + 384 = 0

To solve for W, we can use the quadratic formula:
W = (-b ± sqrt(b² - 4ac)) / (2a)

In our case, a = 2, b = -60, and c = 384.

Calculating the values, we find:
W = (60 ± sqrt((-60)² - 4 * 2 * 384)) / 2 * 2

W = (60 ± sqrt(3600 - 3072)) / 4

W = (60 ± sqrt(528)) / 4

W ≈ (60 ± 22.98) / 4

Therefore, we have two possible values for W:
W1 ≈ (60 + 22.98) / 4 ≈ 20.25
W2 ≈ (60 - 22.98) / 4 ≈ 9.75

Now, substituting these values back into the equation L + W = 30, we can calculate the corresponding values for L:

L1 ≈ 30 - 20.25 ≈ 9.75
L2 ≈ 30 - 9.75 ≈ 20.25

Therefore, the possible dimensions of the garden are:
9.75 yards by 20.25 yards
20.25 yards by 9.75 yards

To find the possible dimensions of the garden, we need to set up equations based on the given information and solve them.

Let's denote the width of each rectangular section as "w" and the length as "l". Since the garden is divided into two equal parts, the dimensions of each section will be the same.

We know that the perimeter of a rectangle is given by the formula: P = 2w + 2l.

Given that the gardener has 120 yards of fence, we can set up the equation: 2w + 2l = 120.

Furthermore, the area of a rectangle is given by the formula: A = w * l.

Given that the area of the entire plot is 384 square yards, we can set up the equation: w * l = 384.

Now we have a system of equations:

Equation 1: 2w + 2l = 120
Equation 2: w * l = 384

To solve this system of equations, we can use substitution or elimination. Let's solve it using substitution.

Rearrange Equation 1 to solve for one variable in terms of the other:
2w = 120 - 2l
w = 60 - l

Substitute this value of "w" into Equation 2:
(60 - l) * l = 384

Expand and rearrange this equation:
60l - l^2 = 384
l^2 - 60l + 384 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, the equation factors easily with integers:

(l - 24)(l - 16) = 0

To find the possible values of "l", we set each factor equal to zero and solve for "l":

l - 24 = 0 => l = 24
l - 16 = 0 => l = 16

Now we have two possible values for the length "l": 24 yards or 16 yards.

Substitute these values back into Equation 1 to find the corresponding width "w":

For l = 24:
w = 60 - 24 = 36

For l = 16:
w = 60 - 16 = 44

Therefore, the possible dimensions of the garden are 36 yards by 24 yards or 44 yards by 16 yards.