A farmer has 100metres of wire fencing from which to build a rectangular chicken run.He intends using two adjacent walls for two sides of the rectangular enclosure.
Detrmine a formula for the enclosed area in terms of x
x * (100-x) = Area
To determine the formula for the enclosed area in terms of x, we need to first understand the given information.
The farmer has 100 meters of wire fencing, and he intends to use two adjacent walls for two sides of the rectangular enclosure. This implies that the length of the rectangular chicken run will be equal to the total length of the wire fencing.
Let's assign variables to the dimensions of the rectangular chicken run. We'll use "x" to represent the length of one of the adjacent walls, and "y" to represent the length of the other two walls.
Based on the information given, we know that the perimeter of the rectangular chicken run must equal the length of the wire fencing, which is 100 meters. Perimeter is calculated by adding up all the sides of a shape.
The perimeter formula for a rectangle is:
Perimeter = 2x + 2y
Since the farmer is using two adjacent walls for two sides of the rectangular enclosure, we can express the perimeter formula as:
2x + y + y = 100
Simplifying the equation, we have:
2x + 2y = 100
Divide both sides by 2:
x + y = 50
Now, let's express the area of the rectangular chicken run in terms of x. The formula to calculate the area of a rectangle is the product of its length and width:
Area = x * y
To determine y in terms of x, we can rearrange the equation x + y = 50 to solve for y:
y = 50 - x
Substituting this value of y in the area formula, we get:
Area = x * (50 - x)
Therefore, the formula for the enclosed area in terms of x is:
Area = x(50 - x)