Elissa wants to set up a rectangular dog run in her backyard. she has 32 feet of fencing to work with and wants to use it all. if the dog run is to be x feet long, express the area of the dog run as a function of x. perhaps jumping up the points will get answers.

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:

Given that:

--- the perimeter of the fence

Represent

length

width

The perimeter of a rectangular fence is calculated as:

So, we have:

Divide both sides by 2

Make y the subject

The area (A) of the fence is:

So, we have:

Substitute

So, the area as a function of x is:

Read more about area and perimeters at:

link

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