Question

Point D is the centroid of △ABC . Find CD and CE . DE=9

Answer 1

CD=18 and CE=18.

The centroid of a triangle is a point of concurrency of its medians. The medians divide each other into segments with a ratio of 2:1, where the longer segment is closer to the vertex. Let's consider triangle

ABC with centroid D.

Given that

DE=9 and D is the centroid, we can use the median property to find CD and CE.

Since DE is one-third of the median from vertex A, we can express

AD as 3×DE:

AD=3×DE=3×9=27

Now, since CD and CE are the other two medians, we can express them in terms of AD as follows:

CD =
`(2)/(3)` AD

CD =
`(2)/(3)` x 27 = 18

CE =
`(2)/(3)` AD

CE = =
`(2)/(3)` x 27 = 18

Therefore, CD=18 and CE=18.