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
50m , 50m
To determine the formula for the enclosed area, let's break down the problem.
1. We know that the farmer has 100 meters of wire fencing.
2. He intends to use two adjacent walls for two sides of the rectangular enclosure.
3. Let the length of the rectangular enclosure be x meters.
Now, let's calculate the perimeter of the enclosure to determine the remaining length of wire fencing:
- Two adjacent walls will use 2x meters of wire fencing.
- As the rectangular enclosure has four sides, the remaining two sides will require 100 - 2x meters of wire fencing.
Considering the enclosed area, it is equal to the product of the length (x) and width (100 - 2x):
Area = x * (100 - 2x)
Therefore, the formula for the enclosed area (A) in terms of x is:
A(x) = x * (100 - 2x)
To determine a formula for the enclosed area in terms of x, we need to understand the given information and constraints.
It is given that the farmer has 100 meters of wire fencing, and he intends to use two adjacent walls for two sides of the rectangular enclosure. This means that the length of the enclosure will be equal to two sides of the enclosure, which we will represent as x meters each, and the width of the enclosure will be the remaining side, which we will represent as y meters.
Considering the wire fencing length, we can set up the following equation:
2x + y = 100
Simplifying this equation, we can express y in terms of x:
y = 100 - 2x
Now, to find the formula for the enclosed area, which is the product of length and width, we multiply x and y:
Area = x * y
Substituting the value of y from the equation above:
Area = x * (100 - 2x)
So, the formula for the enclosed area in terms of x is:
Area = 100x - 2x^2