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!