The value of x is 8.
Solution:
Given ΔVDG [tex]\sim[/tex] ΔVNQ
ND = 15, DG = 60, NQ = 48, NV = x + 4
To find the value of x:
If two triangles are similar then their corresponding sides are in the same ratio.
[tex]$\Rightarrow \frac{DG}{NQ} =\frac{DN}{NV}[/tex]
[tex]$\Rightarrow \frac{60}{48} =\frac{15}{x+4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow {60} \times(x+4)=15 \times 48[/tex]
[tex]$\Rightarrow {60} \times(x+4)=720[/tex]
Divide by 60 on both sides of the equation.
[tex]$\Rightarrow x+4=12[/tex]
Subtract 4 from both sides of the equation.
[tex]$\Rightarrow x=8[/tex]
Hence the value of x is 8.
