Find the value of x please and thank you

Given:

In triangle DEF, HG is parallel to DF.

To find:

The value of x.

Solution:

In triangles DEF and GEH,

[tex]\angle DE F\cong \angle GEH[/tex]          (Common angle)

[tex]\angle EDF\cong \angle EGH[/tex]          (Corresponding angle)

[tex]\Delta DE F\sim \Delta GEH[/tex]             (By AA property of similarity)

We know that corresponding sides of similar triangle are proportional.

[tex]\dfrac{DE}{GE}=\dfrac{DF}{GH}[/tex]

[tex]\dfrac{9+(x+5)}{x+5}=\dfrac{12}{6}[/tex]

[tex]\dfrac{x+14}{x+5}=2[/tex]

[tex]x+14=2(x+5)[/tex]

[tex]x+14=2x+10[/tex]

Isolating variable terms, we get

[tex]x-2x=-14+10[/tex]

[tex]-x=-4[/tex]

[tex]x=4[/tex]

Therefore, the value of x is equal to 4.

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