https://file.aiquickdraw.com/mathbot/file/1725580476489ahkfc2qo.jpg

This is a right triangle problem. To find the value of \( x \), we can use the **Pythagorean theorem**, which states:

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

Where:
- \( a \) and \( b \) are the lengths of the two legs (sides adjacent to the right angle),
- \( c \) is the hypotenuse (the side opposite the right angle).

From the image:
- One leg is 5,
- The other leg is 8,
- \( x \) represents the hypotenuse.

Let's apply the Pythagorean theorem:

\[
x^2 = 5^2 + 8^2
\]

Calculating this:

\[
x^2 = 25 + 64 = 89
\]

Thus, \( x = \sqrt{89} \).

The correct answer is **option D: \( x = \sqrt{89} \)**.

Would you like more details or have any other questions? Here are some related questions:

1. How is the Pythagorean theorem applied in real-world scenarios?
2. What are the conditions for using the Pythagorean theorem?
3. How can you simplify square roots like \( \sqrt{89} \)?
4. How do you solve a right triangle if given two angles and one side?
5. Can the Pythagorean theorem be extended to three dimensions?

**Tip**: Always check that the triangle is a right triangle before applying the Pythagorean theorem!

Find the value of x in a right triangle with legs of lengths 5 and 8, using the given multiple-choice options.

Learn how to solve for the hypotenuse in a right triangle with side lengths of 5 and 8 using the Pythagorean theorem. This problem includes multiple-choice options and a step-by-step solution. Suitable for students in Grades 6-8.

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