Find the value of x please and thank you

Question

asked Mar 5, 2022 190k views

1 Answer

Cleared · Answer 1 · 2022-03-11T02:29:09+0000

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.