Question

A polygon has perimeter 12. It is dilated with a scale factor of k and the resulting image has a perimeter of 8. What is the

scale factor?

Oa

4

3

Oь

LF| G | - | G එය |

Ос

2

Answer 1

The scale factor is 2.

Explanation:

Let the original perimeter of the polygon be P and the scale factor be k. Then, the perimeter of the dilated image is kP.

We are given that the original perimeter is 12 and the perimeter of the dilated image is 8. Therefore:

P = 12

kP = 8

Dividing the second equation by the first, we get:

kP/P = 8/12

k = 2/3

So the scale factor is 2/3. However, the question asks for the "dilation factor," which is the factor by which the original length was multiplied to get the new length. In other words, it is the reciprocal of the scale factor. So:

dilation factor = 1/k = 1/(2/3) = 3/2

Therefore, the answer is not one of the given options.