Answer:
The dimensions of the area will be 8 ft x 40 ft
Step-by-step explanation:
Area and Perimeter
The perimeter can be understood as the distance measured around a shape. The area gives us the idea of the space occupied by the shape. Being w and l the width and length of a rectangle, the perimeter and areas can be computed as follows
[tex]A=wl[/tex]
[tex]P=2w+2l[/tex]
The dog trainer has 96 ft of fencing to cover a [tex]320 ft^2[/tex] rectangular area. This means that
[tex]wl=320[/tex]
[tex]2w+2l=96[/tex]
A system of equations is formed
[tex]\left\{\begin{matrix}wl=320\\ 2w+2l=96\end{matrix}\right[/tex]
We divide the last equation by 2
[tex]w+l=48[/tex]
solve for w
[tex]w=48-l[/tex]
Replacing in the first equation
[tex](48-l)l=320[/tex]
Operating and arranging
[tex]l^2-48l+320=0[/tex]
[tex](l-8)(l-40)=0[/tex]
We have two possible answers
[tex]l=8,\ l=40[/tex]
Which gives us
[tex]w=40,\ w=8[/tex]
In any case, the dimensions of the area will be 8 ft x 40 ft
