Question

Gina has 440 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

Answer 1

Answer:

THerefore, the area would be 12,100 square yards

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

THerefore, the area would be 12,100 square yards