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The problem provided is a right triangle with legs measuring 9 and 12, and you are asked to find the hypotenuse \( x \).

To solve this, we can use the **Pythagorean Theorem**, which states that:

\[
a^2 + b^2 = c^2
\]

where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.

Given:
- \( a = 9 \)
- \( b = 12 \)

Let's substitute these values into the formula:

\[
9^2 + 12^2 = x^2
\]

\[
81 + 144 = x^2
\]

\[
225 = x^2
\]

Now, take the square root of both sides:

\[
x = \sqrt{225} = 15
\]

So, the length of the hypotenuse \( x \) is **15**.

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions you might find interesting:
1. How does the Pythagorean Theorem apply to non-right triangles?
2. What are the other properties of a right triangle?
3. How can you use trigonometry to solve for unknown sides in a triangle?
4. What is the relationship between the sides and angles in any triangle?
5. How do you find the area of a right triangle using its sides?

**Tip**: Always check if a triangle is a right triangle before applying the Pythagorean Theorem!

For the following right triangle, find the side length x. The triangle has legs of 9 and 12.

Learn how to solve for the hypotenuse of a right triangle with legs measuring 9 and 12 using the Pythagorean Theorem. This step-by-step solution demonstrates the application of the formula a^2 + b^2 = c^2, and is suitable for students in Grades 7-10.

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