line CD is a median of angle ABC and M is the centroid, If CM = 14 what is CD
To find the length of CD, we need to understand the properties of medians and centroids.
In a triangle, a median is a line segment that connects a vertex to the midpoint of the opposite side. The centroid is the point of intersection of the three medians, and it divides each median in the ratio 2:1.
In the given scenario, line CD is a median of angle ABC, and M is the centroid. This means that CM represents two-thirds of the entire median CD.
Given that CM = 14, we can set up the following equation:
CM = (2/3)CD
Substituting the value of CM as 14, we have:
14 = (2/3)CD
To solve for CD, we need to isolate it on one side of the equation. Multiply both sides of the equation by 3/2 to cancel out the fraction:
14 * (3/2) = CD
Simplifying the equation:
21 = CD
Therefore, the length of CD is 21 units.