The value of x is 8.
Solution:
Given [tex]\triangle V D G \sim \triangle V N Q[/tex].
DG = 60, NQ = 48, DN = 15, NV = x + 4
To find the value of x:
Property of similar triangle:
If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.
[tex]$\Rightarrow\frac{DG}{NQ} =\frac{DN}{NV}[/tex]
[tex]$\Rightarrow\frac{60}{48} =\frac{15}{x+4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow60(x+4)=15\times48[/tex]
[tex]$\Rightarrow60x+240=720[/tex]
Subtract 240 from both side of the equation.
[tex]$\Rightarrow60x+240-240=720-240[/tex]
[tex]$\Rightarrow60x=480[/tex]
Divide by 60 on both sides of the equation.
[tex]$\Rightarrow\frac{60x}{60} =\frac{480}{60}[/tex]
[tex]$\Rightarrow x=8[/tex]
Hence the value of x is 8.
