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The total land area of the US is 3,531,905 square miles. One 50th of that is 70,638.1 square miles. According to a highly reputable wikipedia article I found, North Dakota has the land area closest to that, at 69,001 square miles.
If you use the exclusive economic zone, and compare one 50th of that to the total area of the states, Minnesota is closest, instead.
South Dakota
No, I’m not showing my work.
Wolfram alpha is good for stuff like that and they make it pretty easy