Let 'a', 'b' and 'c' represent the sides of the triangle and a>b>c (c is the shortest side).

The perimeter is 104:

a + b + c = 104

One side of triangle is 6 more than 3 times the shortest side:

a = 6 + 3c

The third side is 23 centimeters more than the shortest side side:

b = 23 + c

We have the following system of equations:

a + b + c = 104
a = 6 + 3c
b = 23 + c

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click here to see the system of equations solved for a, b and c

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a = 51 cm

b = 38 cm

c = 15 cm

The three sides are 51 cm, 38 cm and 15 cm.