This is a right triangle with one side labeled $9$, the base labeled $12$, and the hypotenuse labeled $x$. To find the missing length $x$, we use the Pythagorean Theorem:

$x^2 = a^2 + b^2$

Where:

• $a = 9$,
• $b = 12$,
• $x$ is the hypotenuse.

Step-by-Step Solution:

1. Substitute the known values: $x^2 = 9^2 + 12^2$

2. Calculate the squares: $x^2 = 81 + 144$

3. Add the results: $x^2 = 225$

4. Solve for $x$ by taking the square root: $x = \sqrt{225} = 15$

Final Answer:

$x = 15$

Would you like a detailed explanation of the steps or help with related concepts?

Related Questions:

1. How is the Pythagorean Theorem derived geometrically?
2. Can the theorem be used in non-right triangles?
3. What is the relationship between the sides in a 3-4-5 triangle?
4. How do you calculate the hypotenuse if one side is unknown?
5. What are some real-world applications of the Pythagorean Theorem?

Tip:

Always verify that the triangle is a right triangle before using the Pythagorean Theorem. Look for a $90^\circ$ angle!