Question

In Upper Delta DEF​, the midpoint of the side opposite vertex D is M and the centroid is C. If DM is 60​, what are DC and​ CM?

Answer 1

`\boxed{\boxed{DC=40,CM=20}}`

Explanation:

The midpoint of the side opposite vertex D is M. So DM is a median to the base EF.

We know that,

The centroid cuts every median in the ratio 2:1

Hence,
`DC=2CM`

Given that, the length of DM is 60​.

`\Rightarrow DM=60`

`\Rightarrow DC+CM=60`

`\Rightarrow 2CM+CM=60`

`\Rightarrow 3CM=60`

`\Rightarrow CM=20`

So,
`DC=2CM=2* 20=40`