Question

Pat wants to create s rectangular playpen for her dogs in her backyard. And estimates the dogs will need 600 square feet. She also wants the length of the playpen to be 30 feet longer than the width, so they have room to run around. What dimensions should the playpen be?

Answer 1

I found width=13.72 ft and length=43.72 ft.
Call one dimension of the rectangle x, the other will be x+30
You want an area A=600 ft^2 but A=length x width=x*(x+30)=600
Rearranging you get:
$x^{2} +30x-600=0$
solving this quadratic equation you get a negative solution and a positive one that gives your result.