We appreciate your visit to Pentagon E is a scaled copy of Pentagon D Determine the scale factor that transforms Pentagon D to Pentagon E based on the following measurements. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine the scale factor that takes pentagon D to pentagon E, we need to compare corresponding side lengths of the two pentagons.
We're given some side lengths for both pentagons:
- For pentagon D: 5.7, 7.5, 12.4
- For pentagon E: 7.6, 9.3, 10
A scale factor is found by dividing a side length in pentagon E by the corresponding side length in pentagon D. Since we have a list of corresponding sides, we must ensure we are comparing the right pairs. However, for this exercise, we can test the potential matches to find a consistent scale factor that works for all sides for which we have measurements.
Let's calculate the scale factors by comparing three given pairs:
Scale factor using the pair (5.7 and 7.6):
[tex]\text{Scale factor} = \frac{7.6}{5.7} \approx 1.3333[/tex]
Scale factor using the pair (9.3 and 7.5):
[tex]\text{Scale factor} = \frac{9.3}{7.5} \approx 1.24[/tex]
Scale factor using the pair (10 and 12.4):
[tex]\text{Scale factor} = \frac{10}{12.4} \approx 0.8065[/tex]
In this example, we have different scale factors calculated depending on chosen side lengths, so we would need the correct corresponding side lengths to be identified or more consistent data to confirm the correct scale factor.
From the information given, it seems we might need a clarification regarding the correct pairs since the calculated scale factors are inconsistent. Typically, if two shapes are similar, the scale factor should be consistent across all corresponding side pairs.
Therefore, with consistent correspondence across the side lengths, the student should re-evaluate based on the actual correct match of sides or verify with additional information which lengths are directly corresponding.
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