Answer: The value of x is 12 units and the scale factor is \(\dfrac{4}{3}.\)
Step-by-step explanation: Given that the triangle DEF is similar to the triangle RST.
We are to find the value of x and the scale factor of the dilation.
We know that the corresponding sides of the similar triangles are proportional.
So, we must have
\(\dfrac{DE}{RS}=\dfrac{EF}{ST}\\\\\\\Rightarrow \dfrac{3}{x}=\dfrac{4}{16}\\\\\\\Rightarrow \dfrac{3}{x}=\dfrac{1}{4}\\\\\Rightarrow x=3\times4\\\\\Rightarrow x=12.\)
The scale factor is given by
\(S=\dfrac{\textup{length of a side of the dilated triangle}}{\textup{length of the corresponding side of the original triangle}}\\\\\\\Rightarrow S=\dfrac{RS}{DE}\\\\\\\Rightarrow S=\dfrac{4}{3}.\)
Thus, the value of x is 12 units and the scale factor is \(\dfrac{4}{3}.\)
