Question

Find the value of x please and thank you

Answer 1

Given:

In triangle DEF, HG is parallel to DF.

To find:

The value of x.

Solution:

In triangles DEF and GEH,

`\angle DE F\cong \angle GEH` (Common angle)

`\angle EDF\cong \angle EGH` (Corresponding angle)

`\Delta DE F\sim \Delta GEH` (By AA property of similarity)

We know that corresponding sides of similar triangle are proportional.

`(DE)/(GE)=(DF)/(GH)`

`(9+(x+5))/(x+5)=(12)/(6)`

`(x+14)/(x+5)=2`

`x+14=2(x+5)`

`x+14=2x+10`

Isolating variable terms, we get

`x-2x=-14+10`

`-x=-4`

`x=4`

Therefore, the value of x is equal to 4.