The lengths of the three sides of a triangle are $7$, $x+4$ and $2x+1$.  The perimeter of the triangle is 36.  What is the length of the longest side of the triangle?
Since the perimeter of the triangle is 36, then $7+(x+4)+(2x+1)=36$ or $3x+12=36$ or $3x=24$ or $x=8$.

Thus, the lengths of the three sides of the triangle are $7$, $8+4=12$ and $2(8)+1=17$, of which the longest is $\boxed{17}.$