To find the length of the hypotenuse in a 45-45-90 triangle when each of its legs has a length of 6 units, we can follow the properties of this special type of right triangle. Here is a step-by-step solution:
1. Understand the Properties of a 45-45-90 Triangle:
A 45-45-90 triangle is an isosceles right triangle where the two legs are of equal length. The relationship between the legs and the hypotenuse in this type of triangle can be described as follows:
[tex]\[
\text{Hypotenuse} = \text{Leg length} \times \sqrt{2}
\][/tex]
2. Identify the Given Leg Length:
Given that each leg of the triangle measures 6 units, we will use this length to find the hypotenuse.
3. Apply the Formula:
Using the relationship for a 45-45-90 triangle:
[tex]\[
\text{Hypotenuse} = 6 \times \sqrt{2}
\][/tex]
4. Calculate the Exact Form (if needed in a simplified form):
To express the hypotenuse in its exact form:
[tex]\[
6 \sqrt{2}
\][/tex]
5. Compare with the Provided Options:
The answer choices are:
A. [tex]\(6 \sqrt{2}\)[/tex] units
B. 6 units
C. [tex]\(3 \sqrt{2}\)[/tex] units
D. 12 units
From our calculation, the hypotenuse is [tex]\(6 \sqrt{2}\)[/tex], which matches option A.
Therefore, the length of the hypotenuse is:
A. [tex]\(6 \sqrt{2}\)[/tex] units
