To find the value of $x$ in this triangle, we need to use the properties of right triangles and the Pythagorean theorem.

Given:

• The left segment has a length of 5.
• The right segment has a length of $x$.
• The hypotenuse has a length of $x + 2$.

Let's denote the height of the right triangle from the right angle to the hypotenuse as $h$.

By the Pythagorean theorem for the two smaller right triangles: $h^2 + 5^2 = (x + 2)^2$ $h^2 + x^2 = (x + 2)^2$

Rewriting the equations:

1. $h^2 + 25 = (x + 2)^2$
2. $h^2 + x^2 = (x + 2)^2$

Since both equations equal $(x + 2)^2$, we can set them equal to each other: $h^2 + 25 = h^2 + x^2$

Cancelling $h^2$ from both sides: $25 = x^2$

Solving for $x$: $x = \sqrt{25}$ $x = 5$

Therefore, the value of $x$ is 5.

Would you like more details or have any questions?

Here are 5 questions you might consider asking next:

1. How do you derive the Pythagorean theorem?
2. Can you solve another geometric problem involving triangles?
3. How do you find the height in an isosceles triangle?
4. Can you explain the properties of special right triangles?
5. How can we apply trigonometry to solve triangle problems?

Tip: In problems involving right triangles, the Pythagorean theorem is a powerful tool to determine the relationship between the sides. Always ensure that the triangle is a right triangle before applying the theorem.