This triangle is a right triangle, with one leg measuring 9, the hypotenuse measuring 13, and the other leg marked as $x$. To solve for $x$, we will use the Pythagorean theorem:

$a^2 + b^2 = c^2$

Here:

• $a = 9$,
• $b = x$,
• $c = 13$ (the hypotenuse).

Substitute the values into the equation:

$9^2 + x^2 = 13^2$

$81 + x^2 = 169$

$x^2 = 169 - 81$

$x^2 = 88$

$x = \sqrt{88}$

Simplify $\sqrt{88}$:

$x = \sqrt{4 \cdot 22} = 2\sqrt{22}$

Thus, $x = 2\sqrt{22}$, or approximately $x \approx 9.38$.

Would you like more details or help with understanding this process?

Here are some related questions to explore:

1. How can you calculate the area of this triangle?
2. What are some real-world applications of the Pythagorean theorem?
3. How would you find the perimeter of this triangle?
4. Could you solve for $x$ using trigonometric ratios?
5. What is the approximate decimal value of $\sqrt{22}$?

Tip: Always check if the triangle fits the right triangle rules before applying the Pythagorean theorem!