Question

In the diagram below of triangle EFG, H is a midpoint of EF and J is a midpointof FG. If HJ = 9x – 19, and EG = 54 – 5x, what is the measure of HJ?

Answer 1

It is given that H is the midpoint of EF and J is the midpoint of FG. So from triangle midpoint theorem, we have,

`HJ=(1)/(2)EG`

Substituting the values,

`\begin{gathered} 9x-19=(1)/(2)(54-5x) \\ 18x-38=54-5x \\ 18x+5x=54+38 \\ 23x=92 \\ x=4 \end{gathered}`

Thus, x = 4 , therefore HJ is,

`9*4-19=17`

Thus, HJ is 17