The value of x is 40.
Solution:
Given ΔVDG and ΔVNG are similar triangles.
DG = 207, NQ = 138, GQ = 60, QV = x
To find the value of x.
In two triangles are similar, then the measures of the corresponding sides are in proportional to each other.
[tex]$\Rightarrow\frac{DG}{NQ}=\frac{GQ}{QV}[/tex]
Substitute the given values.
[tex]$ \Rightarrow\frac{207}{138}=\frac{60}{x}[/tex]
Do cross multiplication, we get
[tex]$ \Rightarrow{207\times x}=138\times60[/tex]
[tex]$ \Rightarrow{207\times x}=8280[/tex]
Divide by 207 on both sides of the equation, we get
[tex]$ \Rightarrow x=\frac{8280}{207}[/tex]
[tex]$ \Rightarrow x=40[/tex]
Hence the value of x is 40.
