To find the perimeter of the triangle in the image, we need to add the lengths of all three sides of the triangle. The three sides are:

1. $x + 1$ (the left side)
2. 4 (the right side)
3. 5 (the bottom side)

The formula for the perimeter $P$ of a triangle is the sum of its side lengths: $P = \text{side 1} + \text{side 2} + \text{side 3}$

So, in this case: $P = (x + 1) + 4 + 5$

Now, let's simplify: $P = x + 1 + 4 + 5 = x + 10$

Thus, the simplified perimeter is $x + 10$.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the perimeter change if the side $x+1$ became $x+2$?
2. What would the area of this triangle be if we know the height?
3. Can you solve for $x$ if the perimeter is given as 20?
4. How would the perimeter formula change for different polygons (like a square or rectangle)?
5. What if the triangle were an equilateral triangle? What would the equation for its perimeter be?

Tip: Always combine like terms when simplifying polynomials to make your final expressions easier to interpret.