Question

A dog trainer has 96 ft of fencing that will be used to create a rectangular work area. Encloses area of 320 ft^2. What will be the dimensions of the area

Answer 1

The dimensions of the area will be 8 ft x 40 ft

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

`A=wl`

`P=2w+2l`

The dog trainer has 96 ft of fencing to cover a
`320 ft^2` rectangular area. This means that

`wl=320`

`2w+2l=96`

A system of equations is formed

`\left\{\begin{matrix}wl=320\\ 2w+2l=96\end{matrix}\right`

We divide the last equation by 2

`w+l=48`

solve for w

`w=48-l`

Replacing in the first equation

`(48-l)l=320`

Operating and arranging

`l^2-48l+320=0`

`(l-8)(l-40)=0`

We have two possible answers

`l=8,\ l=40`

Which gives us

`w=40,\ w=8`

In any case, the dimensions of the area will be 8 ft x 40 ft