We know the perimeter formula would be 1200=2x+2y. And the area will be A=x*y We can to take the derivative of the area formula to find where it is a max but we must first substitute something in from the first formula so we only have one variable.
1200-2x=2y 600-x=y
A=(x)*(600-x) A=600x-x^2
Now we take the derivative: A'=600-2x (set equal to 0 and solve) 0=600-2x 2x=600 x=300
Then when we plug this into the perimeter formula, we can solve for y 1200=2x+2y 1200=2(300)+2y 1200=600+2y 600=2y y=300
So both the length and width are 300 yards, and the area would be 90,000 square yards
