Question

In the diagrams below, ABC is similar to RST. Use a proportion with sides AB and RS to find the scale factor of ABC to RST. Show your work.

Answer 1

Answer:

The scale factor of triangle ABC to triangle RST is 1/3

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ----> the scale factor

To find the scale factor divide the length side of the image (reduced triangle) by the corresponding length side of the pre-image (original triangle)

$z=\frac{RS}{AB}$

substitute the values

$z=\frac{6}{18}$

simplify

$z=\frac{1}{3}$

The scale factor is less than 1

so

Is a reduction

Answer 2

Answer:  The required scale factor of ΔABC to ΔRST is $\dfrac{1}{3}.$

Step-by-step explanation:  Given that triangles ABC and RST are similar, where

AB = 18, BC = 15, AC = 9 and RS = 6.

We are use a proportion with sides AB and RS to find the scale factor of triangle ABC to triangle RST.

We know that the scale factor of dilation is given by

$S=\dfrac{\textup{length of a side of dilated triangle}}{\textup{length of the corresponding side of the original triangle}}.$

Since AB and RS are corresponding sides of the two similar triangle ABC and RST, so the scale factor of ABC to RST is

$S=\dfrac{RS}{AB}\\\\\\\Rightarrow S=\dfrac{6}{18}\\\\\\\Rightarrow S=\dfrac{1}{3}.$

Thus, the required scale factor of ΔABC to ΔRST is $\dfrac{1}{3}.$