Find the scale factor where the pre-image is the small triangle and the image is the large triangle.

Scale factor is the ratio of two corresponding sides.

Here we have two triangles, where the preimage is the smaller triangle and the image is the larger triangle.

So scale factor =14/18 = 7/9

And to find the missing variable, we need to set the ratio.

7/9 = 28/x

Cross multiplying both sides

7x = 28*9

x = 36

 The required scale factor is

Step-by-step explanation:  We are given to find the scale factor of the dilation from the small triangle to the large triangle.

We know that

scale factor of dilation is given by

From the given picture, we have

D = 21 units and O = 27 units.

Therefore, the scale factor of dilation is given by

Thus, the required scale factor is