Question

If HF=4x+9, EF=5x + 3, and FG EH, solve for X (pictures included)

Answer 1

`\boxed{\textsf{ The value of x is \textbf{6}}}.`

Explanation:

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

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

`\sf \triangle EGF \cong HGF`

So we can say that

• EF = HF ( by cpct )

Using this equation we have ,

`\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}}`