6.4 Ratio of perimeters of similar plane figures.

6.4 Ratio of perimeters of similar plane figures.
If two figures are similar, then the ratio of their perimeters is equal to ratio of their corresponding side lengths
Example
Assume that ∆ABC~∆DEF and the ratio of the lengths of their sides is 2. Then, find the ratio of the corresponding perimeters.
Solution:
The perimeter of ∆ABC = 6 + 8 + 10 = 24 and the perimeter of ∆DEF = 3 + 4 + 5 = 12.
"Perimeter of ∆ABC" /"Perimeter of ∆DEF" = 24/12=2 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑠𝑖𝑑𝑒𝑠(𝐴𝐵/𝐷𝐸=𝐵𝐶/𝐸𝐹=𝐴𝑐/𝐷𝐹)
𝐴𝐵/𝐷𝐸 is the same as AB:DE. Both refer to the ratio of 𝐴𝐵 𝑡𝑜 𝐷E
Example
Find the ratio (purple to blue) of the perimeters of the similar rectangles below if the lengths of the rectangles are 4cm and 6cm for purple and blue, respectively.
Solution:
"Perimeter of the Purple rectangle" /P"erimeter of the blue rectangle" =4/6= 2/3