Is it possible to form a square who's area is 18 by connecting four lattice points? Explain.

My teacher told me the side lengths must equal the square root of 18, which I understand. However, I'm not sure where to go from there.

Question

Is it possible to form a square who's area is 18 by connecting four lattice points? Explain. 

My teacher told me the side lengths must equal the square root of 18, which I understand. However, I'm not sure where to go from there.

asnaseer · Answer

first - do you understand what lattice points are?

anonymous · Answer

Yes. I usually describe them as "integer points" but yes, I know what they are.

asnaseer · Answer

so the question is, can you draw a square on set of integer grid points such that each corner of the square is on one of these points and its area is 18.
you are correct in saying that each side length would have to be equal to $\sqrt{18}=\sqrt{9*2}=3\sqrt{2}$

anonymous · Answer

Yes, but I'm not sure that lattice points would work in this case...

asnaseer · Answer

the way to solve this is to draw just one quarter of the square that includes one of the side lengths, as follows:
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