Find the Median to Hypotenuse: Right Triangle with Side Length 10

Question

Given the right triangle

Given the size of the string in the triangle is 10.

Find the size of the median to the hypotenuse.

00:07 Let's figure out the length of BD.

00:10 Here's what we know. According to the data, this is the side length we have.

00:20 BD is the median. A median cuts the side it's drawn to in half.

00:29 Look, it's a right triangle in the example we have.

00:33 In right triangles, the median to the hypotenuse is half as long as the hypotenuse.

00:41 Now, let's plug in the AC value and solve for BD.

00:51 And there you have it. That's the solution!

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.