Answer:
93.75 feet and 187.5 feet
Step-by-step explanation:
Let the width of the rectangular area be x feet and the length be y feet. A farmer with 750 feet of fencing wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the rectangle. So, there will be 4 widths and 2 lengths, thus
[tex]4x+2y=750\\ \\2x+y=375\\ \\y=375-2x[/tex]
Find the area:
[tex]A(x)=x\cdot y=x\cdot (375-2x)=375x-2x^2[/tex]
Find the derivative:
[tex]A'(x)=375-2\cdot 2x=375-4x[/tex]
Equate it to 0:
[tex]375-4x=0\\ \\4x=375\\ \\x=93.75\ feet\\ \\y=375-2\cdot 93.75=187.5\ feet[/tex]
