The length of a median of a triangle is 36 units. How many units from the vertex is the median?
Your question does not make sense as worded. The median PASSES THROUGH the vertex, so there is no distance between them.
The median is a line from a vertex to the midpoint of the opposite side. All triangles have three medians. They intersect at one point, called the centroid.
What you or your teacher may be really asking is how far from the vertex is from the CENTROID (sometimes called "median point").
There is a theorem that says that the centroid is 2/3 of the length of the median from the vertex. That would make the answer to your question 24 units.
http://mathworld.wolfram.com/TriangleCentroid.html
To find the length of a median of a triangle and the distance from the vertex to the median, we need to understand what a median is.
A median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. It divides the triangle into two equal areas.
In this case, we are given that the length of the median is 36 units. To find the distance from the vertex to the median, we need to determine the length of the entire median as well as the length of the segment from the vertex to the midpoint.
To find the length of the entire median, we can use the formula:
Length of Median = (1/2) * Length of Side Opposite the Vertex
Let's assume the length of the side opposite the vertex is 'x'. So, according to the formula:
36 = (1/2) * x
To find 'x', we can multiply both sides of the equation by 2:
2 * 36 = x
72 = x
Therefore, the length of the side opposite the vertex is 72 units.
Now, since the median divides the triangle into two equal areas, the length of the segment from the vertex to the midpoint will be half the length of the median. Therefore, the distance from the vertex to the median is:
(1/2) * 36 = 18 units
So, the median is 36 units in length, and the distance from the vertex to the median is 18 units.