The question is about Similar Figures. The sides of similar pentagons will have a constant ratio, which can be found by dividing the side length of the smaller pentagon by the larger one. For example, if the smaller side is 3 units and the larger side is 6 units, the ratio is 0.5, meaning each side of the larger pentagon is twice the length of the corresponding side in the smaller pentagon.
In mathematics, similar figures are geometric shapes that have the same shape but may differ in size. These figures have corresponding angles that are equal, and their sides are proportional. When you compare two similar figures, you can use a scale factor to relate the lengths of corresponding sides. This concept is crucial in geometry and real-world applications such as map scaling, model making, and architecture. Similar figures help mathematicians and scientists analyze and solve problems involving relationships between objects of varying sizes with similar shapes.
The question is about similar pentagons. Similar figures have the same shape, but are not necessarily the same size. Therefore, the ratio of corresponding sides in similar figures is constant. Let's say the side of the smaller pentagon is 'a' and the side of the larger pentagon is 'b'. So the ratio 'a/b' is the same for all corresponding sides. If you know the length of the sides of the small and large pentagon, you can calculate this ratio by dividing the side length of the small pentagon by the side length of the large pentagon. For example, if the small pentagon has a side of 3 units and the larger pentagon has a side of 6 units, the ratio is 3/6 = 0.5. Therefore, each side of the larger pentagon is twice the length of the corresponding side in the smaller pentagon.
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Answer:
The scale factor is 2.2
Step-by-step explanation:
To find the scale factor, you look at the length of any two sides that correspond to each other. For example, in the diagram we can see that the side with the length of 4 on the smaller pentagon corresponds to the side with the length of 8.8 on the larger pentagon.
To find the scale factor, you divide the length of the side of the larger pentagon, by the length of the side of the smaller pentagon.
[tex]\frac{8.8}{4} = 2.2[/tex]
The scale factor is 2.2
Hope this helps!
