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.
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.
To represent the area that can be enclosed in terms of X, we can use the formula for the area of a rectangle: A = L * W.
Let's assume that the length of the rectangle is X meters (since it is the only variable given), and the width of the rectangle is Y meters.
Now, let's use the given information: the perimeter of the rectangle is 100 meters. The perimeter of a rectangle is given by the formula: P = 2L + 2W.
We know that the total length of the sides adjacent to the river is X, and there are two of these sides, so the total length of these sides is 2X.
The remaining two sides perpendicular to the river must add up to 100 - 2X to complete the perimeter.
Therefore, the equation for the perimeter of the rectangle becomes:
2X + 2(100 - 2X) = 100.
Simplifying the equation gives us:
2X + 200 - 4X = 100.
Combining like terms:
-2X + 200 = 100.
Subtracting 200 from both sides of the equation:
-2X = -100.
Now, divide both sides by -2 to solve for X:
X = (-100) / (-2).
Simplifying further gives us:
X = 50.
Now, substitute X = 50 into the formula for the area of a rectangle:
A = L * W = X * Y.
Therefore, the function A that represents the area that can be enclosed in terms of X is:
A = 50 * Y.
To find a function A that represents the area that can be enclosed, we need to consider the given information.
We have 100 meters of fencing available to enclose a rectangular area next to a river. Remember that a rectangle has two equal lengths opposite each other, which will be perpendicular to the length of the river.
Let's denote the length of the rectangle as L and the width as W.
Since the fence needs to go around the entire rectangle, we have the equation:
2L + W = 100
However, we want to express the area enclosed in terms of a single variable, so we need to eliminate one of the variables from the equation.
Let's solve the equation for L in terms of the width W:
2L = 100 - W
L = (100 - W)/2
Now we can express the area A as the product of length and width:
A = L * W
A = [(100 - W)/2] * W
Therefore, the function A that represents the area that can be enclosed in terms of the width variable W is:
A(W) = (100 - W)/2 * W