Respuesta :

Answer:

[tex]\boxed{\textsf{ The value of x is \textbf{6}}}.[/tex]

Step-by-step explanation:

Given that in the given figure , HF = 4x + 9 and EF = 5x +3 . And FG [tex]\perp[/tex] EH . we need to find the value of x .

And here the two triangles must be congruent to each other . That is ,

[tex]\sf \triangle EGF \cong HGF [/tex]

So we can say that

  • EF = HF ( by cpct )

Using this equation we have ,

[tex]\sf\implies EF = HF \\\\\sf\implies 4x +9=5x+3\\\\\sf\implies 4x - 5x = 3-9\\\\\sf\implies -x=-6\\\\\sf\implies \boxed{\pink{\sf x = 6}}[/tex]

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