If the width of the paddock is x, this means that the 4 lengths will b x, x, 30-x and 30-x.
I'm sure you know that the area is equal to the width times the length, this gives us the equation .
For part B, imagine that the was a and just sketch how you normally would.
As for the last bit, the best method for this would be calculus, but if you've not learnt it yet then I guess not in this case.
Here's a fact that should help you. For any shape with a set perimeter, the one that will give you the greatest area is the one with all sides equal.
For example, say you have 60 metres of fencing and you want to construct a triangular fence, the shape that will give you the greatest area would be the equilateral triangle, ie the one with all 3 sides 20m.
So if your building a rectangular yard, then the optimum shape would be...?