one hundred meters of fencing is available to enclose a rectangular area next to a river.Give a function A that can represent the are that can be enclosed, in terms of X.
A = x(50-x)
To find a function that represents the area that can be enclosed, we first need to understand the constraints of the problem.
We are given that there are 100 meters of fencing available. This indicates that there are three sides to consider for the rectangular area: the two lengths and one width. The fourth side of the rectangle is formed by the river, meaning we don't need to allocate any fencing material for it.
Let's assume that the length of the rectangle is denoted by "l" meters, and the width is denoted by "w" meters.
To enclose the rectangular area, we would need two lengths and two widths, which gives us the equation for the total amount of material used for the fencing:
2l + 2w = total fencing material used
Since we know that the total fencing material available is 100 meters, we can rewrite the equation as:
2l + 2w = 100
Now, let's solve this equation to express either "l" or "w" in terms of the other variable. We'll solve it for "w".
2l + 2w = 100
2w = 100 - 2l
w = 50 - l
Now that we have expressed width "w" in terms of length "l", the final step is to find the area "A" in terms of "l".
The area of a rectangle is given by the formula:
A = length * width
Substituting the expression for "w" into the equation:
A = l * (50 - l)
Thus, the function A that represents the area that can be enclosed in terms of the length "l" is:
A(l) = l * (50 - l)