1. **Problem:** Find the perimeter of triangle $\triangle MNP$ where sides are given as $5x - 34$, $25$, and $22$, and angle at $P$ is $x + 4$. We need to find the perimeter in terms of $x$. 2. **Formula:** The perimeter $P$ of a triangle is the sum of the lengths of its sides: $$P = MN + NP + PM$$ 3. **Substitute the given side lengths:** $$P = (5x - 34) + 25 + 22$$ 4. **Simplify the expression:** $$P = 5x - 34 + 25 + 22$$ $$P = 5x + ( -34 + 25 + 22 )$$ $$P = 5x + 13$$ 5. **Final answer:** The perimeter of $\triangle MNP$ is $$\boxed{5x + 13}$$ Note: Since no value of $x$ is given, the perimeter is expressed in terms of $x$.