Suppose you have 76 feet of fencing to enclose a rectangular dog pen. the function a=38x - x^2 where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area? round to the nearest tenth as necessary.

a.) width = 19 ft; area = 1083 ft2

b.) width = 19 ft; area = 361 ft2

c.) width = 38 ft; area = 361 ft2

d.) width = 38 ft; area = 760 ft2

Option B is correct

width = 19 ft; area = 361

Step-by-step explanation:

For a quadratic equation:

            .....[1]

the axis of symmetry is given by:

As per the statement:

The function is given by:

         .....[2]

where,

x is the width of the rectangular dog pen.

On comparing the given equation with [1] we have;

a = -1  and b = 38

then;

⇒

Simplify:

x = 19 ft.

Substitute in [2] to find the maximum area:

Therefore, 19 ft width gives you the maximum area and the maximum area is, 361 square ft.