https://file.aiquickdraw.com/mathbot/file/1728572719686ibzpr7lq.jpg

The triangle in the image is a 45°-45°-90° triangle, which is a special right triangle. In this type of triangle, the two legs are equal in length, and the relationship between the legs and the hypotenuse follows the ratio \( 1:1:\sqrt{2} \).

From the image:
- The hypotenuse is given as \( \sqrt{18} \).

To find the length of the leg \( s \), we can use the following formula for 45°-45°-90° triangles:

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

Given that the hypotenuse is \( \sqrt{18} \), we substitute this into the formula:

\[
\sqrt{18} = s \times \sqrt{2}
\]

Now, solve for \( s \):

\[
s = \frac{\sqrt{18}}{\sqrt{2}} = \frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9} = 3
\]

So, the length of leg \( s \) is \( 3 \).

The correct answer is **D. 3**.

Would you like more details or have any further questions?

Here are 5 related questions you might find interesting:
1. How is the ratio \( 1:1:\sqrt{2} \) derived for a 45°-45°-90° triangle?
2. Can the Pythagorean theorem be used to verify the result for a 45°-45°-90° triangle?
3. How do special right triangles differ from general right triangles?
4. What are the properties of other special triangles, such as 30°-60°-90° triangles?
5. How can you generalize the formula for finding the legs of a right triangle given different angles?

**Tip:** In 45°-45°-90° triangles, knowing one leg allows you to find both the other leg and the hypotenuse easily using simple ratios!

What is the length of leg s of the triangle below?

Learn how to find the length of the leg in a 45°-45°-90° triangle where the hypotenuse is given as sqrt(18). This problem uses the special right triangle theorem and helps you understand key geometric concepts. Suitable for students in Grades 8-10.

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