7. A wire of length $150 \mathrm{~cm}$ is to be cut into $n(n>2)$ segments, each of which has an integer length of no less than $1(\mathrm{~cm})$. If no three segments can form a triangle, then the maximum value of $n$ is $\qquad$ .
7. 10 First, $n$ should be as large as possible, which means the length of each segment must be as small as possible. The lengths of these small segments can only be $1,1,2,3,5,8$, $13,21,34,55,89, \cdots$, but $1+1+2+\cdots+34+55=143$ 150 , so the maximum value of $n$ is 10.