Math Problem Statement

What’s the scaled factor

What is the scale factor between two rectangles where the original rectangle has sides 2 and 3 units, and the scaled copy has a side of 4 units?

Solution

To determine the scale factor, you need to compare the corresponding sides of the original rectangle and the scaled copy.

From the image:

  • The height of the original rectangle is 2 units, and the height of the scaled copy is 4 units.

The scale factor is calculated as:

Scale factor=Dimension of scaled copyDimension of original=42=2\text{Scale factor} = \frac{\text{Dimension of scaled copy}}{\text{Dimension of original}} = \frac{4}{2} = 2

So, the scale factor is 2.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. What happens to the area of the rectangle when you apply the scale factor of 2?
  2. If another dimension of the original rectangle is 5 units, what would be its corresponding dimension in the scaled copy?
  3. How do you calculate the scale factor if only the area is given for both the original and scaled copies?
  4. Can the scale factor ever be less than 1? What does it represent?
  5. How do you find the scale factor if you are given the perimeter of both the original and scaled shapes?

Tip: The scale factor applies uniformly to all dimensions, meaning both width and height are multiplied by the same number when scaling.

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Math Problem Analysis

Mathematical Concepts

Geometry
Scaling
Ratios

Formulas

Scale factor = Dimension of scaled copy / Dimension of original

Theorems

Scaling theorem (uniform scaling of figures)

Suitable Grade Level

Grade 6