Answer:
The length of 20 feet and width of 40 feet will result in the least amount of fencing.
Step-by-step explanation:
Please find the attachment.
Let w represent width and l represent length of the rectangle.
We have been given that a rectangular area against a wall is to be fenced off on the other three sides to enclose 800 square feet.
We know that area of rectangle is width times length that is:
This is our constraint equation.
We can see from the attachment that the fencing would be for 3 sides that is:
This is our objective equation.
From constraint equation, we will get:
Substitute this value in objective equation:
Let us find the derivative of objective equation.
Now, we will set the derivative equal to 0 to solve for length:
Cross multiply:
Take positive square root:
Upon substituting in , we will get:
Therefore, the length of 20 feet and width of 40 feet will result in the least amount of fencing.