You have 332 feet of fencing to enclose a rectangular region. what is
the maximum area?

a. 6889 square feet

b. 6885 square feet

c. 110,224 square feet

d. 27,556 square feet

Option A is correct

The maximum area is, 6889 square feet

Step-by-step explanation:

Perimeter of a rectangle is given by:

where,

l is the length and w is the width of the rectangle respectively.

As per the statement:

You have 332 feet of fencing to enclose a rectangular region.

⇒ feet

Then using perimeter formula:

Divide both side by 2 we get;

or

                 .....[1]

Area of a rectangle(A) is given by:

                    .....[2]

Substitute the value of [1] in [2] we have;

⇒

We have to find the maximum area:

A quadratic equation then the axis of symmetry is given by:

The maximum  area occurs at:

feet

Substitute the value of w in [1] we have;

feet

Substitute the value of l and w in [2] we have;

square feet

therefore, the maximum area is, 6889 square feet