The value of x is 15.
Solution:
Given ΔPQR [tex]\sim[/tex] ΔUTV.
If two triangles are similar, then the corresponding parts are congruent.
[tex]$\Rightarrow \frac{PR}{UV} =\frac{RQ}{VT}[/tex]
[tex]$\Rightarrow \frac{14}{x + 6} =\frac{8}{x -3}[/tex]
Do cross multiplication, we get
⇒ 14(x - 3) = 8(x + 6)
⇒ 14x - 42 = 8x + 48
Add 42 on both sides.
⇒ 14x = 8x + 90
Subtract 8x on both sides.
⇒ 6x = 90
Divide by 6 on both sides.
⇒ x = 15
The value of x is 15.
