Given:
[tex]\Delta DHE\sim \Delta DGF[/tex]
To find:
The value of x.
Solution:
We know that, corresponding sides of similar triangles are proportional.
Since,[tex]\Delta DHE\sim \Delta DGF[/tex], therefore
[tex]\dfrac{HE}{GF}=\dfrac{DE}{DF}[/tex]
On substituting the values from the figure, we get
[tex]\dfrac{8}{12}=\dfrac{x}{x+2}[/tex]
[tex]\dfrac{2}{3}=\dfrac{x}{x+2}[/tex]
On cross multiplication, we get
[tex]2(x+2)=3x[/tex]
[tex]2x+4=3x[/tex]
[tex]4=3x-2x[/tex]
[tex]4=x[/tex]
Therefore, the value of x is 4.
