How Do You Find Missing Measurements of Similar Figures Using a Scale Factor?

Here, 'x' is the length of the longest side of the DEF triangle
Triangle ABC is similar to triangle DEF because all angles are the same
EF and BC are corresponding sides and can be compared using a ratio
The bar over EF and BC means they are line segments
The length of EF is 12, and the length of BC is 6
The greatest common factor of 12 and 6 is 6, so divide both numbers by 6 to get 2/1, or 2
A scale factor of 2 means the sides of triangle DEF are twice those of triangle ABC
We can flip our initial ratio and get the same answer!

1. Here, 'x' is the same as saying 'side DF' of triangle DEF
1. A ratio of corresponding sides will help us find the scale factor between the two triangles
2. The given figures show us that EF=12 and BC=6
3. The sides correspond because they sit between angles with the same measurement
1. Up to this point, our ratio was 12/6
2. The greatest common factor of 12 and 6 is 6, so divide them both by 6 to get 2/1, or 2
3. A scale factor of 2 means triangle DEF is twice as big as triangle ABC
4. So the sides of triangle DEF are twice as long as those of triangle ABC
1. A scale factor of 2 means triangle DEF is twice as big as triangle ABC
2. So the sides of triangle DEF are twice as long as those of triangle ABC
3. That means we can just multiply 8 by 2 to find x
1. Our equation '8•2 = x' simplifies to '16 = x'
2. So 'x', or side DF, has a length of 16!
1. BC/EF = 6/12 ÷ 6/6 = 1/2
2. A scale factor of 1/2 means triangle ABC is half as big as triangle DEF
3. So the sides of triangle ABC are half as long as those of triangle DEF
4. So our equation becomes:
5. 'x•(1/2) = 8'
6. Multiplying both sides of this equation by 2 will cancel 1/2 on the left and we get 'x=16'!

Use a scale factor to find the missing measurement, 'x'.