Final answer:
The ratio of perimeters of similar figures with linear measurements of 9 and 14 is 9/14. The ratio of their areas is (9/14)^2, which simplifies to 81/196. These calculations are based on proportions and similarity principles.
Step-by-step explanation:
To find the values of the ratios (red to blue) of perimeters and areas of similar figures with linear measurements of 9 and 14, we apply concepts of similarity and proportions. The perimeter ratio is the same as the ratio of their corresponding sides since perimeter is a linear measure. Thus, the ratio of perimeters is 9/14, which can be simplified to 9/14 or 0.642857143 when simplified further.
Next, the ratio of areas of similar figures is equal to the square of the ratio of their corresponding linear measurements. Therefore, the ratio of the areas is (9/14)^2. Simplifying that, we get 81/196, which is the simplest form for the area ratio of the similar figures.
If the unit of measure for these figures was explicitly given, we could then maintain consistency in the units when calculating real-world distances or areas, much like when using scale factors for maps or models.