Question

1. Lie on your stomach with your arms by your sides.

2. Lie on your stomach with your hands by your sides.

3. Lie on youir wtomach with your hands on your both sides.

4. Lie on your stomach with your hands on/by your side(s)
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Which one is right? Do we have to use 'by' or 'on'? Do we have to use 'side' or 'sides'?

Answer 1

5. Lie on your face on the floor with your hands by your sides. (What about this one?)

Answer 2

One has (usually) two hands and two sides. "sides" is appropriate. In #3, "both" is redundant. We only have two sides.

"by" and "on" are synonymous in this context.

Answer 3

#5 is fine.

Actually, "by" and "on" are not exactly synonymous. "by" doesn't mean touching your sides; "on" does.