A triangle has a perimeter of 39 cm. The longest side is twice as long as the shortest side. The third side is 7 cm. longer than the shortest side. What are the lengths of the three sides?

Let the shortest side be x cm, so that the longest side is 2x cm, and the third side is x + 7 cm. Since the perimeter of the triangle is 39 cm we have:

x + 2x + x + 7 = 39
4x = 32
x = 8

Thus, the lengths of the sides are 8 cm, 15 cm, and 16 cm.