Answer:
The minimum amount of fence (minimum perimeter) is 240 feet
Step-by-step explanation:
see the attached figure to better understand the problem
Let
x ----> the length of one rectangular lot
y ----> the width of one rectangular lot
we know that
The area of the two rectangular lots is equal to
[tex]A=LW+LW[/tex]
[tex]A=2(1,200)=2,400\ ft^2[/tex]
so
[tex]2,400=2LW[/tex]
[tex]1,200=LW[/tex] -----> [tex]W=\frac{1,200}{L}[/tex] -----> equation A
The perimeter of the two rectangular lots is equal to
[tex]P=4L+3W[/tex] ----> equation B
substitute equation A in equation B
[tex]P=4L+(3)\frac{1,200}{L}[/tex]
Using a graphing tool
Find out the minimum (vertex) of the function
The minimum is the point (30,240)
see the attached figure
therefore
The minimum amount of fence (minimum perimeter) is 240 feet
The length is [tex]L=30\ ft[/tex]
The width is [tex]W=\frac{1,200}{30}=40\ ft[/tex]
