Perimeter Ratio of Similar Figures
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 2: Transformations) learn that similar figures have a perimeter ratio equal to their side length ratio. This direct proportion between corresponding lengths and perimeters lets students find unknown perimeters from known side ratios.
Key Concepts
For similar figures, the ratio of their perimeters equals the ratio of any pair of corresponding side lengths:.
$$\frac{\text{Perimeter of Figure 1}}{\text{Perimeter of Figure 2}} = \frac{\text{Side length of Figure 1}}{\text{Corresponding side length of Figure 2}}$$.
Common Questions
What is the perimeter ratio of similar figures in 7th grade?
For similar figures, the ratio of their perimeters equals the ratio of any pair of corresponding side lengths (the scale factor).
If two similar triangles have sides in ratio 2:3, what is their perimeter ratio?
The perimeter ratio is also 2:3. Both perimeters and side lengths scale by the same factor.
How do you find an unknown perimeter of a similar figure?
Set up a proportion: P1/P2 = s1/s2. Substitute known values and cross-multiply to solve for the unknown perimeter.
What chapter in Big Ideas Math Advanced 2 covers perimeter ratio of similar figures?
Chapter 2: Transformations in Big Ideas Math Advanced 2 (Grade 7) covers perimeter ratio of similar figures.
Why does the perimeter scale by the same factor as side lengths?
Perimeter is the sum of all side lengths. If each side is multiplied by k, the perimeter sum is also multiplied by k.