Final answer:
Using the algebraic method to determine the dimensions of the fence with the given perimeter, the length is found to be 117.5 feet and the width is 107.5 feet.
Step-by-step explanation:
The farmer has 450 feet of fencing to build a fence around his livestock. Since the length of the fence is supposed to be 10 feet longer than the width, we can use algebra to set up the following equations to represent the perimeter (P) of the rectangular fence area: P = 2(length) + 2(width). Here, the length can be represented as width + 10 feet.
Substituting the known values in we get: 450 = 2(width + 10) + 2(width). Simplifying this we have 450 = 4(width) + 20, which leads to 4(width) = 430 after subtracting 20 from both sides. Dividing both sides by 4 to solve for the width, we find width = 107.5 feet.
Finally, the length of the fence is 10 feet longer than the width, which gives us a length of 107.5 + 10 = 117.5 feet. The dimensions of the fence then are a length of 117.5 feet and a width of 107.5 feet.