Question

Three sides of a fence and an existing wall form a rectangular enclosure. the total length of fence used for three sides is 240 ft. write the area function in terms of one variable, then find the domain of that function

Answer 1

Let the length of the side opposite the wall be x, and the lengths of the other 2 sides be y.

x+2y=240     ft

then

2y=240-x
y=(240-x)/2=120-x/2


The area of the rectangular enclosure is determined by the function 
$A(x)=x \cdot y =x \cdot (120-x/2)$      (square feet)


both width and length must be >0, 

so we must have:

i) x>0
ii) 120-x/2>0                 (at the same time)

solving the second inequation:

120-x/2>0

120>x/2

240>x


so x must be smaller than 240, but also larger than 0.


Thus the domain is (0, 240)


Answer: Domain: (0, 240)