Math Problem Statement
Create a scaled copy of the original rectangle with a scale factor of
Create the scaled copy.
Original Rectangle
2
3
Solution
To create a scaled copy of the original rectangle, we need to multiply both the width and height of the original rectangle by the scale factor of 2.
Step-by-Step Solution:
Given:
- Original dimensions: Width = 2, Height = 3
- Scale factor = 2
Scaled dimensions:
- New width =
- New height =
Thus, the dimensions of the scaled rectangle will be:
Final Answer:
The scaled copy of the rectangle has a width of 4 and height of 6.
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5 Follow-up Questions:
- What happens if the scale factor is less than 1 (e.g., 0.5)?
- How would the perimeter and area change after scaling?
- What if we scale with different factors for width and height (non-uniform scaling)?
- Can you scale other shapes, like circles or triangles? How?
- What is the relationship between scaling and similarity of geometric figures?
Tip:
When scaling a 2D shape by a factor , the area changes by a factor of . For example, in this case, the new area will be 4 times the original.
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Math Problem Analysis
Mathematical Concepts
Geometry
Scaling
Proportionality
Formulas
Scaled width = original width × scale factor
Scaled height = original height × scale factor
Theorems
Similarity of geometric figures
Proportional scaling
Suitable Grade Level
Grades 5-7