Answer: The correct option is
(D) 4.
Step-by-step explanation: Given that the two triangles in the figure are similar.
We are to find the scale factor that can be used to find the missing length x.
From the figure, we note that
two pairs of corresponding lengths of the sides of the given triangles are (4, 16) and (6, x).
And, the scale factor is given by
[tex]S=\dfrac{\textup{length of a side of dilated triangle}}{\textup{length of the corresponding side of the original trinagle}}\\\\\\\Rightarrow S=\dfrac{16}{4}\\\\\Rightarrow S=4.[/tex]
Also, we get
[tex]S=\dfrac{x}{6}\\\\\\\Rightarrow 4=\dfrac{x}{6}\\\\\Rightarrow x=24.[/tex]
Therefore, the missing length x is 24 units and the scale factor is 4.
Option (D) is CORRECT.
