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In Triangle FGH, GJ is an angle bisect or of G and perpendicular to FH. What is the length of FH in units?

In Triangle FGH GJ Is An Angle Bisect Or Of G And Perpendicular To FH What Is The Length Of FH In Units class=

Sagot :

Using the perpendicular bisector theorem, we have the following:

[tex]GF=GH[/tex]

then we can write the following equation:

[tex]3x-8=16[/tex]

solving for x, we have:

[tex]\begin{gathered} 3x-8=16 \\ \Rightarrow3x=16+8=24 \\ \Rightarrow x=\frac{24}{3}=8 \\ \\ x=8 \end{gathered}[/tex]

we get x = 8. Then, the length of FH is:

[tex]\begin{gathered} FH=FJ+JH=8+8=16 \\ \Rightarrow FH=16 \end{gathered}[/tex]

therefore, FH = 16

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