To find the length of the longest side of the triangle, I need to know the value of $x$. I can use the fact that the perimeter of the triangle is 36 to write an equation involving $x$. The perimeter is the sum of the lengths of the three sides, so I have $7 + (x+4) + (2x+1) = 36$. Simplifying this equation, I get $3x + 12 = 36$, so $3x = 24$ and $x = 8$. Now that I know $x$, I can plug it into the expressions for the lengths of the three sides. The sides are $7$, $8+4 = 12$ and $2(8) + 1 = 17$. The longest side is $17$, so that is my answer. 
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?