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See if you can visualize how you would build a rectangular paddock using the extremes of each of the choices you were given. Some of the choices won't be possible -- of the ones that are possible the correct answer will be the choice whose domain is the widest set. I'll help you work through the first choice to see if it's possible, and then you try the others and let us know what you think is the right answer.
In choice (a) the domain is (0,200]. Let's start with the lower end of the domain - the "(0" means that the domain starts at 0 but is exclusive of 0 itself - that is, it can be a positive number as close to 0 as you want, but cannot actually be 0. For example perhaps one side is only 0.01 meter, or maybe even smaller, but greater than 0 You could have one side .01 meters, the opposite side would also be .01 meters, and you would have 199.98 meters of fence left over to construct the other two sides - each would be half of that, or 99.99 meters each. This certainly seems possible. But could you build a rectangle paddock where the length of one side is actually equal to 0? That one doesn't seem possible, as then the paddock would actually be two pieces of fence 100 meters long each with no space between them - that's not a rectangle. It's also clear that the value of x can't be negative. So the choice of "(0" at the low end seems like a good choice.
At the high end of choice (a), the value of "200] "means that one side could be as long as 200 meters, inclusive of 200 meters - this can't be right because if you build one side 200 meters long you won't have any fence left over to build the other 3 sides - do you see that? OK, so (a) is not the right choice - now, can you work through the others and post back with the one you think is correct?
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