One hundred meters of fencing is available to enclose a rectangular area next to river give a function

A that can represent the area that can be enclosed, in terms of X?

As solved previously:

Total fence length = 100 m
Total Length of each side perpendicular to river, W = X
Length of side parallel to river, L = 100-2X

Area,
A(X)= length * width
= L*W
= (100-2X)X

Simplify the right hand side to get the final solution.

100x-2x squared

To find the function that represents the area that can be enclosed in terms of x, we need to understand the constraints given in the question.

The question mentions that 100 meters of fencing is available to enclose a rectangular area next to a river.

Let's break down the problem:

1. We need to enclose a rectangular area.
2. The area is next to a river, so one side of the rectangle will be the river.
3. We have 100 meters of fencing available.

Now, let's define the variables:

Let x be the length of the side of the rectangle perpendicular to the river.
Let y be the length of the side of the rectangle parallel to the river.

Since we have 100 meters of fencing available, the sum of all sides of the rectangle should be equal to 100:

2x + y = 100

Now, we need to express the area A in terms of x. The area of a rectangle is given by the product of its sides:

A = x * y

Since we already have an equation with y in terms of x, we can substitute it into the area equation:

A = x * (100 - 2x)
A = 100x - 2x^2

Therefore, the function A(x) that represents the area that can be enclosed in terms of x is:

A(x) = 100x - 2x^2