To find the perimeter of the right triangle shown in the image, we need to sum the lengths of all three sides. The given side lengths are:

• One leg of length $u - 3$
• Another leg of length $4$
• The hypotenuse of length $u - 2$

The formula for the perimeter $P$ of a triangle is:

$P = \text{side}_1 + \text{side}_2 + \text{hypotenuse}$

Step 1: Adding the sides

Using the given side lengths:

$P = (u - 3) + 4 + (u - 2)$

Step 2: Simplify the expression

Combine like terms:

$P = u - 3 + 4 + u - 2 = 2u - 1$

Thus, the perimeter of the triangle is:

$P = 2u - 1$

Let me know if you'd like further explanation or have additional questions!

Relative questions:

1. How do you find the perimeter of a triangle with unknown side lengths?
2. What is the importance of simplifying expressions in geometry?
3. Can you explain how the Pythagorean theorem applies to this triangle?
4. What is the difference between legs and the hypotenuse in a right triangle?
5. How would the perimeter change if $u$ is doubled?

Tip: Always double-check that you’ve combined like terms correctly when simplifying algebraic expressions!