Scale Factor
The scale factor is the ratio of the lengths of two corresponding sides of two polygons that are similar.
You can find the scale factor by finding the ratio of any corresponding sides of similar polygons. So, for the sample above, 
The scale factor is 
.
Similar Polygons and Perimeter
One additional property of similar polygons is if two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
Let's try this with the triangles above. We already know that the ratio of the sides is . What is the ratio of the perimeters?
Use the Scale Factor link to find out more.
Example #3
Find the scale factor of polygon ABCD to polygon GHIJ. Then find the values of x and y.
Solution: In order to find the scale factor, look at the sides lengths that are given to you. Identify two sides that correspond to each other and state the ratio that compares the two figures.
Let's use AD and GJ.
The scale factor is 2.
Now, to solve for x, we just have to set up the ratio of the corresponding sides and set it equal to 2. Roll over each step.
Step 1
Start by setting up a proportion that includes the side with the variable x. That side is CD. IJ is similar to CD, so use those sides with our known ratio, AD/GJ.
: 
Step 2
Substitute in the value of AD/GJ from the previous step
: 
Step 3
Substitute in the measures of CD and IJ
: 
Step 4
Multiply both sides by 8 to eliminate the denominator from the fraction
: 
Step 5 Simplify! : x = 16
To solve for y, we do the same thing. Roll over each step.
Step 1 Start by setting up a proportion that includes the side with the variable y. That side is GH. GH is similar to AB, so use those sides with out known ratio, AD/GJ. : 
Step 2 Substitute in the value of AD/GJ : 
Step 3 Substitute in the measures of AB and GH : 
Step 4 Multiply both sides by y to eliminate the denominator from the fraction : 
Step 5 Divide both sides by 2 to isolate the y : 8 = 2y
Step 6: 4 = y
