Math Problem Statement

The side that corresponds to 4 units in the original rectangle is 1 unit in the scaled copy. What is the scale factor? Original Rectangle Scaled Copy 4 8 1 The scale factor is

Solution

To find the scale factor of the scaled copy, you divide the side length of the scaled copy by the corresponding side length of the original rectangle.

In this case, the side of the original rectangle is 4 units, and the corresponding side in the scaled copy is 1 unit.

The scale factor is calculated as:

Scale factor=Side of scaled copySide of original rectangle=14\text{Scale factor} = \frac{\text{Side of scaled copy}}{\text{Side of original rectangle}} = \frac{1}{4}

Thus, the scale factor is 14\frac{1}{4} or 0.25.

Would you like further details or explanations on this?

Here are 5 related questions to deepen understanding:

  1. What happens to the area of the rectangle when the scale factor is 14\frac{1}{4}?
  2. How would you find the scale factor if the original side was 8 units and the scaled side was 2 units?
  3. How does a scale factor greater than 1 affect the size of a scaled figure?
  4. Can you apply the same scale factor to all dimensions of a 3D shape? Why or why not?
  5. What is the relationship between the scale factor and perimeter of a rectangle?

Tip: A scale factor less than 1 shrinks the figure, while a scale factor

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Math Problem Analysis

Mathematical Concepts

Geometry
Scale Factor
Ratios

Formulas

Scale Factor = (Side of Scaled Copy) / (Side of Original Rectangle)

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 6-8