Parts of a Triangle: Median in a right-angled triangle

To find the length of the median to the hypotenuse in a right triangle, we will follow these steps:

• Step 1: Identify the length of the hypotenuse, $c$, which is given as 10 units.
• Step 2: Use the formula for the median to the hypotenuse: $m = \frac{c}{2}$, where $c$ is the hypotenuse.
• Step 3: Substitute the value of $c$ into the formula to find $m$.

Now, let's perform the calculations:
Since the hypotenuse $c = 10$, substituting $10$ into the formula gives:

$m = \frac{10}{2} = 5$

Thus, the length of the median to the hypotenuse is $5$ units.

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 $c = 12$.