Math Problem Statement

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Create a scaled copy of the original rectangle with a scale factor of 2.

Solution

In this problem, you are asked to create a scaled copy of the original rectangle using a scale factor of 2.

Original Dimensions of the Rectangle:

  • Width: 2 units
  • Height: 3 units

Given Scale Factor:

  • 22

Scaling Process:

To create the scaled copy, we multiply both the width and height of the original rectangle by the scale factor of 2.

  1. Scaled Width:
    2×2=4 units2 \times 2 = 4 \text{ units}

  2. Scaled Height:
    3×2=6 units3 \times 2 = 6 \text{ units}

Conclusion:

The scaled rectangle will have the following dimensions:

  • Width: 4 units
  • Height: 6 units

The scaled copy should be drawn as a rectangle that is twice the size of the original in both directions, horizontally and vertically.

Would you like more details or further clarification? Here are some related questions to deepen your understanding:

  1. How does a scale factor of 2 affect the perimeter of the rectangle?
  2. What happens to the area when you scale the rectangle by a factor of 2?
  3. Can you describe the process for scaling with non-integer scale factors, like 12\frac{1}{2}?
  4. How can you find the inverse of this scaling operation?
  5. What is the general rule for scaling any polygon?

Tip: When scaling a figure, all linear dimensions (like width and height) change by the scale factor, but the area changes by the square of the scale factor!

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Math Problem Analysis

Mathematical Concepts

Geometry
Scaling
Ratios

Formulas

Scaled Width = Original Width × Scale Factor
Scaled Height = Original Height × Scale Factor

Theorems

Scaling Theorem

Suitable Grade Level

Grades 5-7