Let us say length is X and width is Y.

Perimeter `= 2(X+Y) = 3600`

`2(X+Y) = 3600`

`X+Y = 1800`

`Y = 1800-X`

Area` (A) = X*Y = X(1800-X) = 1800X-X^2`

For maximum/minimum area dA/dX = 0

dA/dx = 1800-2X

When `(dA)/(dX) = 0` ;

`1800-2X = 0`

`X = 900`

If X = 900 has a maximum then `(d^2A)/(dX^2)` at X = 900 would be negative.

`(dA)/dx = 1800-2X`

`(d^2A)/dx^2 = -2 ` (negative)

So we have a maximum for the area.

X = 900

Y = 1800-900 = 900

*So the dimensions would be a square with 900ft each side.*

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now