Question

What is the largest area that can be fenced off of a rectangular garden if it will be fenced off with 220 feet of available material?

Answer 1

It will be a square garden.

Let's do the maths:

Let's call the dimensions of the garden `x` and `y`
Then we can immediately get rid of `y` because the circumference of the fence is `220ft`, so:

`2x+2y=220->2y=220-2x->y=110-x`

Now we come to area `A` (substituting `y`)

`A=x*y=x(110-x)=110x-x^2`

To find the maximum we set the derivative to `0`

`A'=110-2x=0->x=55->y=110-55=55`
(see earlier equation)

Answer : Area `A=55*55=3025 ft^2`