the challenge involves in dealing with the owner is to use a 20 meter fencing material to build a pig pen so that the owner will not be buying any additional materials considering also that one side of the pen is the outside wall of his garage? what is the dimension of this pig pen?
Some details of the question appear to be missing.
I'm assuming the pen is to be rectangular and further that you want to find the length and width that enclose the maximum possible area.
Let the width of the pen be x, so that the length is 20-3x the area (y) is:
y = 20 x -2 x^2
y' = 20 -4 x
Maximum area exists when y'=0
Solve for x.
To determine the dimensions of the pig pen using a 20-meter fencing material, we need to consider that one side of the pen is the outside wall of the owner's garage. Let's break down the steps to find the solution:
Step 1: Visualize the pig pen
First, let's visualize the pig pen. We know that one side of the pen is the garage wall. We need to determine the shape and dimensions of the remaining sides of the pen.
Step 2: Calculate the remaining perimeter
Since one side of the pen is the garage wall, we need to calculate the perimeter of the remaining sides that require the fencing material. To do this, we subtract the length of the garage wall from the total perimeter.
Perimeter of the pen = Total perimeter - Length of the garage wall
Step 3: Determine the remaining sides
We need to find the remaining sides' dimensions to calculate their perimeter. This will help us determine the shape and size of the pig pen.
Step 4: Distribute the remaining perimeter
Distribute the remaining perimeter among the sides to create a desirable shape for the pig pen. The dimensions can vary depending on the shape you choose.
Step 5: Calculate the dimensions
Using the distributed perimeter, calculate the dimensions of the remaining sides.
Step 6: Verify the solution
Check if the dimensions of the pig pen obtained in Step 5 will require exactly 20 meters of fencing material. If the perimeter exceeds 20 meters, adjust the dimensions accordingly.
With these steps in mind, you can proceed to calculate the dimensions of the pig pen.