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

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

$A=wl$

$P=2w+2l$

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