Step 1 :Let's denote the shortest side of the triangle as \(x\).
Step 2 :According to the problem, one side is twice the length of the shortest side, so it is \(2x\).
Step 3 :The third side is 18 feet more than the length of the shortest side, so it is \(x + 18\).
Step 4 :The perimeter of a triangle is the sum of the lengths of its sides, so we can write the equation as \(x + 2x + (x + 18) = 154\).
Step 5 :Solving this equation, we find that \(x = 34\).
Step 6 :So, the shortest side of the triangle is \(34\) feet.
Step 7 :The side that is twice the length of the shortest side is \(2x = 68\) feet.
Step 8 :The side that is 18 feet more than the length of the shortest side is \(x + 18 = 52\) feet.
Step 9 :Final Answer: The dimensions of the triangle are \(\boxed{34}\) feet, \(\boxed{68}\) feet, and \(\boxed{52}\) feet.