https://file.aiquickdraw.com/mathbot/file/17286667113954z2t3hq0.jpg

The triangle in the image is a 45°-45°-90° triangle, which is an isosceles right triangle. In such a triangle, the relationship between the legs and the hypotenuse is well known: the hypotenuse \( h \) is \( \sqrt{2} \) times the length of either leg.

### Given:
- Both legs of the triangle have a length of \( 9\sqrt{2} \).

### Hypotenuse calculation:
The formula for the hypotenuse \( h \) in a 45°-45°-90° triangle is:
\[
h = \text{leg} \times \sqrt{2}
\]
Substituting the given leg length of \( 9\sqrt{2} \):
\[
h = 9\sqrt{2} \times \sqrt{2} = 9 \times 2 = 18
\]

Thus, the length of the hypotenuse is **18**, which corresponds to option **E**.

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Would you like more details on the steps, or do you have any questions?

Here are 5 follow-up questions to explore:

1. What is the general formula for the hypotenuse in any 45°-45°-90° triangle?
2. How can you calculate the area of this triangle using the given leg lengths?
3. Why does multiplying \( \sqrt{2} \) by itself result in 2?
4. How does the Pythagorean Theorem apply to this specific triangle?
5. How do other types of special triangles differ from a 45°-45°-90° triangle?

**Tip:** In any 45°-45°-90° triangle, knowing just the length of one leg allows you to determine the entire triangle's dimensions!

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

Solve a 45°-45°-90° triangle problem where both legs are 9√2. Learn how to calculate the hypotenuse using the formula h = leg * sqrt(2) and apply geometric properties to special right triangles. Suitable for Grades 8-10.

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