Math Problem Statement

6. If Rectangle A is a scaled copy of Rectangle C, what is the scale factor? 7. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.

Solution

From the image you provided, we are working on two questions:

  1. If Rectangle A is a scaled copy of Rectangle C, what is the scale factor?
    The answer provided indicates that there is "no scale factor". This might imply that Rectangle A is not a scaled copy of Rectangle C, or there is insufficient data to calculate a scale factor.

  2. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.
    To determine if two rectangles are scaled copies, the ratios of their corresponding sides must be equal. If Rectangle C is not a scaled copy of Rectangle B, the side lengths of Rectangle C and B must not have proportional relationships.
    For example, if the ratio of the width to the height in Rectangle B is different from the ratio in Rectangle C, then Rectangle C is not a scaled copy of Rectangle B.

Would you like help in framing a detailed answer for question 7? Let me know if you have the dimensions or additional information about the rectangles.


Here are 5 related questions to expand the topic:

  1. How do you calculate the scale factor between two rectangles?
  2. What happens if only one pair of sides between two rectangles is proportional?
  3. Can a rectangle be a scaled copy of another if one is rotated?
  4. How does changing only the width or height affect the scale factor between two rectangles?
  5. Why is proportionality important in determining if two figures are scaled copies?

Tip: Always check the ratio of corresponding sides when determining if two shapes are scaled versions of each other.

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Math Problem Analysis

Mathematical Concepts

Geometry
Scale Factor
Proportional Relationships

Formulas

Scale Factor = (Dimension of Copy) / (Dimension of Original)

Theorems

Proportionality Theorem
Similarity of Figures

Suitable Grade Level

Grades 6-8