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A gardener has a rectangular vegetable garden which is 30m long and 12m wide. He traces to alleys x meters wide, similar to this:

_____________________

|________| x |________|

x___________ _________

|________| x |________|

Determine, with x, the area occupied by the alleys and the area occupied by the vegetables.

Determine the possible values of x for the width of the alley so that the area of the alleys is superior to 41 meters squared and so that the cultivated part is superior to 280 meters squared.

Here's what I've got so far:

30-x * 12 - x = cultivated area

360 - 30x - 12x + x = cultivated area

360 - 42x + x squared = cultivated area

So the gardened area is: x squared - 42x

But how do I prove this? Do I need to prove this?

Next, I need help trying to get the values of x. How do I go about doing this?

Sorry if my "garden" is sloppy. I tried to make it look like the book.

Any help is appreciated Thank you