You need to remember the equation that gives the area of rectangle, such that:

`A = l*w`

l represents the length

w represents the width

Since the problem provides the value of perimeter of rectangle, you may write area, either in terms of length, or in terms of width, using the equation of perimeter, such that:

`600 = 2(l + w) => 300 = l + w => l = 300 - w`

Hence, substituting back 300 - w for l in equation of area yields:

`A(w) = (300 - w)*w`

Opening the brackets yields:

`A(w) = 300w - w^2`

You need to maximize the area of rectangle, hence, you need to differentiate the function `A(w) = 300w - w^2` with respect to w, such that:

`A'(w) = (300w - w^2)' => A'(w) = 300*w' - (w^2)'`

`A'(w) = 300*1 - 2w => A'(w) = 300 - 2w`

Now, you need to solve for w the equation `A'(w) = 0` such that:

`300 - 2w = 0 => 2w = 300 => w = 150 m`

**Hence, evaluating the dimensions that maximize the area of the fence, yields `w=l = 150 m` .**