Given:
In [tex]\Delta DE F,EM=12,FJ=60,MK=11[/tex].
M is the centroid of the triangle DEF.
To find:
The lengths of MJ, DM and EL.
Solution:
We know that the centroid is the intersection points of medians of a triangle and centroid divides each median in 2:1.
M is the centroid of the triangle DEF. It means DK, EL, FJ are medians and M divides these segments in 2:1.
It is given that [tex]FJ=60[/tex].
[tex]MJ=\dfrac{1}{2+1}FJ[/tex]
[tex]MJ=\dfrac{1}{3}(60)[/tex]
[tex]MJ=20[/tex]
Therefore, the length of MJ is 20 units.
Let DM and MK are 2a and a. It is given that, [tex]MK=11[/tex]. Then
[tex]a=11[/tex]
Now,
[tex]DM=2a[/tex]
[tex]DM=2(11)[/tex]
[tex]DM=22[/tex]
So, the length of DM is 22 units.
Let EM and ML are 2a and a. It is given that, [tex]EM=12[/tex]. Then
[tex]2a=12[/tex]
[tex]a=\dfrac{12}{2}[/tex]
[tex]ML=6[/tex]
Now,
[tex]EL=EM+ML[/tex]
[tex]EL=12+6[/tex]
[tex]EL=18[/tex]
So, the length of EL is 18 units.
