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

Answer:

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

Step-by-step 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