A rectangular animal pen will be built using 200 meters of fencing. If one side of the rectangle is meters, find the area of then pen.

One side = ? meters

60

Let the length of one side of the rectangle be x meters.

The perimeter of a rectangle is given by the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

In this case, the perimeter is 200 meters, which gives us the equation:

200 = 2(x + w)

Simplifying the equation, we have:

100 = x + w

We need to find the area of the pen, which is given by the formula: A = l * w, where A is the area, l is the length, and w is the width.

Since the width of the rectangle is not provided explicitly, we need to find it in terms of x.

Using the equation 100 = x + w, we can rewrite it as w = 100 - x.

Substituting this expression for w into the area formula, we get:

A = x * (100 - x)

Simplifying further:

A = 100x - x^2

Therefore, the area of the pen can be expressed as A = 100x - x^2.

To find the area of the rectangular pen, we need to determine the length and width of the rectangle.

Let's call the length of the rectangle "L" and the width "W". We are given that one side of the rectangle is "X" meters.

Now, let's start by setting up the equation for the perimeter of the rectangle using the given information. The perimeter of a rectangle is the sum of all its sides.

Perimeter of the rectangle = 2L + 2W

We know that the total length of the fencing is 200 meters. So, we can write the equation as:

2L + 2W = 200

Now, let's consider the given information that one side of the rectangle is "X" meters. Since we have the length and width, we can write the equation as:

L + 2W = X

Now, let's solve these equations to determine the values of L and W.

From the previous equation, we can rewrite it as:

L = X - 2W

Substituting this value of L into the equation for the perimeter of the rectangle:

2(X - 2W) + 2W = 200

Expanding and simplifying:

2X - 4W + 2W = 200

2X - 2W = 200

Now, let's solve for W:

2W = 2X - 200

W = (2X - 200) / 2

Simplifying:

W = X - 100

Now, we have the value of W in terms of X. We can substitute this value into the equation for the area of the rectangle to find the final answer.

Area of the rectangle = Length × Width = L × W = (X - 2W) × W

Substituting the value of W:

Area = (X - 2(X - 100)) × (X - 100)

Simplifying further:

Area = (X - 2X + 200) × (X - 100)

Area = (-X + 200) × (X - 100)

Now, we have the equation for the area of the rectangular pen in terms of X. To find the specific value of the area, we need to know the value of X, which is not provided in the question.