Sure, let's solve this problem step-by-step.
We are given a 45-45-90 triangle where each leg has a length of 6 units.
### Step-by-Step Solution:
1. Understanding the 45-45-90 Triangle:
In a 45-45-90 triangle, the two legs are equal in length, and the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of one leg. This comes from the properties of 45-45-90 triangles.
2. Given Data:
Each leg of the triangle is 6 units long.
3. Formula for Hypotenuse:
The length of the hypotenuse (h) in a 45-45-90 triangle is given by the formula:
[tex]\[
h = \text{leg length} \times \sqrt{2}
\][/tex]
4. Substitute the given leg length into the formula:
[tex]\[
h = 6 \times \sqrt{2}
\][/tex]
5. Simplify the expression:
[tex]\[
h = 6 \sqrt{2}
\][/tex]
So, the length of the hypotenuse in this 45-45-90 triangle is [tex]\( 6 \sqrt{2} \)[/tex] units.
### Conclusion:
The correct answer is:
C. [tex]\( 6 \sqrt{2} \)[/tex] units.
