https://file.aiquickdraw.com/mathbot/file/1728593127610x48ibqk4.jpg

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.

Find the perimeter of a triangle with sides labeled x+1, 4, and 5. Simplify your answer.

Learn how to find the perimeter of a triangle with polynomial expressions for side lengths. This problem involves simplifying polynomial expressions and understanding the concept of perimeter. Suitable for Grade 8 students.

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