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I hope there is a process of solving high school math problems and finding mn length.
Take the midpoint L of FG, then ML= 1.

NG=0.5, GL=0.5, then NL= 0.5 =0.705 under the radical sign, you should have learned Pythagorean theorem, right?

Because ML is perpendicular to the bottom surface EHGF, ML is perpendicular to NL.

According to Pythagorean theorem, the square of MN = the square of NL+the square of ML =0.5+ 1= 1.5.

So MN= 1.5= 1.224 under the root sign.

So choose one