domain of the area

Question

A farmer has 1000 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A?

Answer 1

Perimeter = length + length + width + width 

 

1000 = 2*length + 2*x

2*length = 1000 - 2*x

length = 500 - x

 

A = length * width = (500 - x)*x = -x^2 + 500*x  

 

The length and width must both be positive  ==> 

x > 0  and 

500 - x > 0  ==>  x < 500 

 

So the domain of A is 0 < x < 500 or (0,500) in interval notation