The perimeter of a fence, is the sum of its side lengths.
The length of the fence is: [tex]\mathbf{6k^3 + 9k^2- 15k + 10}[/tex]
The perimeter is given as:
[tex]\mathbf{P = w(k) + 2[f(k) + g(k)]}[/tex]
So, we have:
[tex]\mathbf{P = k^2 - 3k + 2 + 2[k^3 + 4k^2 - 6k + 2k^3 + 4]}[/tex]
Simplify
[tex]\mathbf{P = k^2 - 3k + 2 + 2[3k^3 + 4k^2 - 6k + 4]}[/tex]
Open brackets
[tex]\mathbf{P = k^2 - 3k + 2 + 6k^3 + 8k^2 - 12k + 8}[/tex]
Collect like terms
[tex]\mathbf{P = 6k^3 + k^2 + 8k^2- 3k - 12k + 2 + 8}[/tex]
[tex]\mathbf{P = 6k^3 + 9k^2- 15k + 10}[/tex]
Hence, the length of the fence is: [tex]\mathbf{6k^3 + 9k^2- 15k + 10}[/tex]
Read more about perimeters at:
https://brainly.com/question/6465134
