Answer:
Step-by-step explanation:
Let the length be x and the width be y
The perimeter of a rectangle is give as ; 2 ( L + B) , that is
We know the perimeter formula would be 440=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.
440-2x=2y
220-x=y
A=(x)*(220-x)
A=220x-x^2
Now we take the derivative:
A'=220-2x (set equal to 0 and solve)
0=220-2x
2x=220
x=110
Then when we plug this into the perimeter formula, we can solve for y
440=2x+2y
440=2(110)+2y
440=220+2y
220=2y
y=110
So both the length and width are 110 yards, and the area would be 12,100 square yards
