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 = 2×2=42 \times 2 = 4
  • New height = 3×2=63 \times 2 = 6

Thus, the dimensions of the scaled rectangle will be:

New Width=4,New Height=6\text{New Width} = 4, \quad \text{New Height} = 6

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:

  1. What happens if the scale factor is less than 1 (e.g., 0.5)?
  2. How would the perimeter and area change after scaling?
  3. What if we scale with different factors for width and height (non-uniform scaling)?
  4. Can you scale other shapes, like circles or triangles? How?
  5. What is the relationship between scaling and similarity of geometric figures?

Tip:

When scaling a 2D shape by a factor kk, the area changes by a factor of k2k^2. 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