Answer: 19.84 cm and 20.51 cm
Other answers are possible as long as they are between 19 cm and 21 cm inclusive.
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Step-by-step explanation
The lower bound is 20*(1-0.05) = 19
The upper bound is 20*(1+0.05) = 21
5% of 20 = 0.05*20 = 1 cm represents the max error possible in either direction. The student's recorded measurement is somewhere between 19 cm and 21 cm.
Two possible values the student recorded are 19.84 cm and 20.51 cm
Infinitely many other answers are possible. Just make sure the values are between 19 and 21 inclusive. Something like 16 cm is too short, while 39 cm for example is too long. Draw out a number line if it helps you visualize what's going on.