The first part is 9 cm long while the other is 18 cm long


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Let x be the smaller part
             since, the problem says that the bigger part is twice as long as the other,
                  so the bigger part should be twice x or 2x so:

If you add x and 2x, it becomes 27, so the equation is:

x + 2x = 27 cm
3x = 27 cm
3x (1/3) = 27 cm ( 1/3)
3/3x = 27 cm / 3
x = 9 cm
2x = 18 cm

So the 2 parts are:   9 cm and 18 cm.