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.

$\dfrac{DE}{GE}=\dfrac{DF}{GH}$

$\dfrac{9+(x+5)}{x+5}=\dfrac{12}{6}$

$\dfrac{x+14}{x+5}=2$

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

$x+14=2x+10$

Isolating variable terms, we get

$x-2x=-14+10$

$-x=-4$

$x=4$

Therefore, the value of x is equal to 4.