7. (10 points) There is an octagon, each of whose sides has a length that is an integer number of centimeters. If any three sides taken from this octagon cannot form a triangle. Then the shortest perimeter of an octagon that meets these conditions is $\qquad$ cm.
【Analysis】The Fibonacci sequence, starting from the third term, each term is equal to the sum of the two preceding ones. Any three numbers taken as the sides of a triangle cannot form a triangle, which leads to the conclusion.

【Solution】According to the problem, the side lengths of the octagon satisfy the Fibonacci sequence. When the perimeter of the octagon is the shortest under these conditions, the side lengths are $1,1,2,3,5,8,13,21$, and the perimeter is $54 \mathrm{~cm}$. Therefore, the answer is 54.