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If DM=60 find DC and CM
(with shown work please)

If DM=60 find DC and CM (with shown work please)-example-1
User Tamika
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The centroid of a triangle divides each median into a 2:1 ratio.

In triangle DEF, DC = 40 and CM = 20.

In triangle DEF, C is the centroid and DM = 60. Find DC and CM.

A centroid of a triangle is a special point where the medians of the triangle intersect. Each median divides the triangle into two triangles with equal areas. In other words, the centroid divides each median into a 2:1 ratio, where the longer segment is the one that connects the centroid to the vertex.

Knowing that DM = 60 and that C is the centroid, we can use the 2:1 ratio to find the lengths of DC and CM.

DC: Since DC is the longer segment of the median DM, we can set up the following proportion:

DC/CM = 2/1

We can then plug in the known value of DM (60) to solve for DC:

DC = (2/3) * DM

DC = (2/3) * 60

DC = 40

CM: Once we know DC, we can find CM using the same proportion:

CM = DC / 2

CM = 40 / 2

CM = 20

Therefore, DC = 40 and CM = 20.

User Sharaya
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