To find: The function that models the length of fencing required to build a rectangular pen whose area is .
The function that models the length of fencing is .
Let the dimension of the rectangular pen be x and y.
Perimeter (length of fencing) of rectangular pen is,
Area of rectangular fence is product of its dimensions.
Substitute 100 for Area in above equation and get y in terms of x.
Divide the above equation by x.
Summarize the information in the table as shown below.
|In Words||In Algebra|
|Length of fencing|
|Length of rectangular pen.|
|Width of the rectangular pen|
Use the information and model the function.
Thus, the function that models the length of fencing is .
To find: The dimension of pen that requires minimum amount of fencing.
The dimension of fencing for minimum length is 10 m by 10 m.
The function that models the length of fencing as calculated in part (a) is,
Sketch the graph of length function as shown below.
Observe from Figure (1) that function attains a minimum value when x is 10.
Substitute 10 for x in equation (2) and solve for y.
The value of y is .
Thus, the dimension of fencing for minimum length is 10 m by 10 m.
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!