Question

A dog trainer has 104 ft of fencing that will be use to create a rectangular work area for dogs. If the trainer wants to enclose an area of 576 ft sq, what will be the dimensions of the work area.

Answer 1

The dimensions of the work area are 16 ft by 36 ft

Explanation:

Let

x ----> the length of the work area in feet

y-----> the width of the work area in feet

we know that

The perimeter of the work area is equal to

`104=2(x+y)`

simplify

`52=(x+y)`

`y=52-x` ----> equation A

The area of the work area is equal to

`576=xy` ---> equation B

substitute equation A in equation B

`576=x(52-x)`

`576=52x-x^2`

`x^2-52x+576=0`

solve the quadratic equation by graphing

using a graphing tool

The solutions are

x=16 ft, y=36 ft

or

x=36 ft, y=16 ft

see the attached figure

therefore

The dimensions of the work area are 16 ft by 36 ft