Question

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

Answer 1

6889 square feet
Letter A

Answer 2

Option A is correct

The maximum area is, 6889 square feet

Explanation:

Perimeter of a rectangle is given by:

`P = 2(l+w)`

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.

⇒
`P = 332` feet

Then using perimeter formula:

`332 =2(l+w)`

Divide both side by 2 we get;

`166 = l+w`

or

`l=166-w` .....[1]

Area of a rectangle(A) is given by:

`A = lw` .....[2]

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

`A = (166-w)w`

⇒
`A = 166w -w^2`

We have to find the maximum area:

A quadratic equation
`y=ax^2+bx+c` then the axis of symmetry is given by:

`x = -(b)/(2a)`

The maximum area occurs at:

`w = -(166)/(2(-1)) = (166)/(2) = 83` feet

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

`l = 166-83 = 83` feet

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

`A_(max) = 83 \cdot 83 = 6889` square feet

therefore, the maximum area is, 6889 square feet