A(x) = x(16 -x)
Area is the product of length and width. If the length is x, then the width will be half of the total perimeter less the two sides of length x, (32-2x)/2 = 16-x.
So, the area is ...
... A = length · width
... A(x) = x(16 -x)
_____
If you like, you can expand this to ...
... A(x) = -x² +16x
The area of a rectangular figure is calculated by multiplying the length and the width of the figure. So, the area as a function of x is: [tex]A(x) = x(16 - x)[/tex]
Given that:
[tex]P = 32[/tex] --- the perimeter of the fence
Represent
[tex]x \to[/tex] length
[tex]y \to[/tex] width
The perimeter of a rectangular fence is calculated as:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
So, we have:
[tex]P= 2 \times (x+ y)[/tex]
[tex]32= 2 \times (x+ y)[/tex]
Divide both sides by 2
[tex]16= x+ y[/tex]
Make y the subject
[tex]y = 16 - x[/tex]
The area (A) of the fence is:
[tex]Area = Length \times Width[/tex]
So, we have:
[tex]A = x \times y[/tex]
Substitute [tex]y = 16 - x[/tex]
[tex]A = x \times (16 - x)[/tex]
[tex]A = x(16 - x)[/tex]
So, the area as a function of x is:
[tex]A(x) = x(16 - x)[/tex]
Read more about area and perimeters at:
https://brainly.com/question/1633440
