Given:
The two triangles are similar by SSS.
To find:
The value of x.
Solution:
If two triangles are similar to each other by SSS, then the corresponding sides of the triangles are proportional.
It is given that [tex]\Delta ABC\sim \Delta DE F[/tex]. So,
[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}[/tex]
[tex]\dfrac{9}{6}=\dfrac{12}{8}=\dfrac{3(x-1)}{x+1}[/tex]
[tex]\dfrac{3}{2}=\dfrac{3}{2}=\dfrac{3x-3}{x+1}[/tex]
[tex]\dfrac{3}{2}=\dfrac{3x-3}{x+1}[/tex]
On cross multiplication, we get
[tex]3(x+1)=2(3x-3)[/tex]
[tex]3x+3=6x-6[/tex]
[tex]3x-6x=-3-6[/tex]
[tex]-3x=-9[/tex]
Divide both sides by -3.
[tex]x=3[/tex]
Therefore, the value of x is 3.
