Question

A rectangular field is to be enclosed with 400 meters of fencing material. If we let x be the length of the field, express its area in square meters in terms of x. Identify the domain of the function representing the area and show that it is continuous on its domain.

Answer 1

if x is the length, let y be the width
2x + 2y = 400
x + y = 200
y = 200-x

area = xy
= x(200-x) <---- from here you can see that 0 < x < 200
= 200x - x^2