Question

Given ΔDEF : ΔRST, find the scale factor.

Answer 1

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 $\dfrac{4}{3}.$

Answer 2

The scale factor of DEF : RST is 3/4.

X = 12