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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?

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 class=

Respuesta :

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

[tex]HJ=\frac{1}{2}EG[/tex]

Substituting the values,

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

Thus, x = 4 , therefore HJ is,

[tex]9\times4-19=17[/tex]

Thus, HJ is 17

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