https://file.aiquickdraw.com/mathbot/file/1728572816450hab6s103.jpg

The triangle shown in the image is a 45°-45°-90° special right triangle. For this type of triangle, the lengths of the sides follow a specific ratio:

- The legs are equal in length.
- The hypotenuse is equal to the length of one leg multiplied by \(\sqrt{2}\).

### Given:
- Length of each leg = \( 3\sqrt{2} \).

### Finding the hypotenuse:
Using the formula for a 45°-45°-90° triangle:

\[
\text{Hypotenuse} = \text{Leg} \times \sqrt{2}
\]

\[
\text{Hypotenuse} = 3\sqrt{2} \times \sqrt{2} = 3 \times 2 = 6
\]

Thus, the length of the hypotenuse is **6**.

The correct answer is:
- **A. 6**

Would you like further details or have any other questions? 

### Related Questions:
1. What is the ratio of the sides in a 30°-60°-90° triangle?
2. How do you derive the side length ratios for a 45°-45°-90° triangle?
3. Can you solve for the hypotenuse if only one leg is given for a 45°-45°-90° triangle?
4. How can we determine the hypotenuse if one leg is missing in a right triangle?
5. What is the general Pythagorean theorem formula used for any right triangle?

**Tip:** Remember that the 45°-45°-90° triangle is an isosceles right triangle, making its two legs equal and the hypotenuse \(\sqrt{2}\) times the length of each leg.

What is the length of the hypotenuse of the triangle below?

Learn how to calculate the hypotenuse of a special 45°-45°-90° right triangle where both legs are 3√2 units long. This solution involves using the formula for this triangle type, which states that the hypotenuse is leg times √2. Suitable for Grade 9-10 students.

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