Right Triangle Problem: Finding Hypotenuse from 6-Unit Median

To solve this problem, we'll follow these steps:

• Step 1: Identify the key formula for medians in right triangles.
• Step 2: Apply this formula to find the hypotenuse length.
• Step 3: Verify that the result matches one of the given choices.

Now, let's work through each step:

Step 1: In a right triangle, the median from the right angle vertex to the hypotenuse equals half of the hypotenuse length. That is, if the length of the median is denoted as $m = \frac{c}{2}$, where $c$ is the hypotenuse length.

Step 2: The given length of the median is 6. Thus, we have:

$6 = \frac{c}{2}$

Multiplying both sides by 2 gives:

$c = 2 \times 6 = 12$

Step 3: The calculated hypotenuse length is 12. We check the answer options provided and find that 12 is indeed one of the given choices.

Therefore, the solution to the problem is $c = 12$.