Question

In CDE, J is the centroid. If JF=15 find EJ

Answer 1

From the figure, J is the centroid. Hence, the lines DH, FE and CG are medians.

Therefore, we can apply the 2/3 rule, that is, the centroid is 2/3 of the way from the vertex to the opposite midpoint.

In other words, we can write

`JE=(2)/(3)FE`

since, we know that FE=FJ+JE, we have

`JE=(2)/(3)(FJ+JE)`

and, from this equation we can find JE since FJ=15:

`JE=(2)/(3)(15+JE)`

The, we obtain

`\begin{gathered} JE=(2)/(3)(15)+(2)/(3)JE \\ JE-(2)/(3)JE=(2)/(3)(3\cdot5) \\ \end{gathered}`

in which we moved (2/3)JE to the left hand side and we wrote 15 as 3*5. Now, it reads

`\begin{gathered} (3)/(3)JE-(2)/(3)JE=2\cdot5 \\ (1)/(3)JE=10 \\ JE=3\cdot10 \\ JE=30 \end{gathered}`

Therefore, JE=EJ=30.