Let x be the shortest side of the triangle. Then the other side is 8x/3. The perimeter of the triangle is the sum of all three sides, so we have:
x + 84 + 8x/3 = 282
Multiplying both sides by 3, we get:
3x + 252 + 8x = 846
11x = 594
x = 54
So the shortest side of the triangle is 54 cm. The longest side is 8x/3 = 144 cm.