The rectangles below are scaled copies of one another. The side that corresponds to 10 units in the original rectangle is 5 units in the scaled copy.

Question

To find the scale factor, determine the number you can multiply each side length of the original rectangle by to find the corresponding side length in the scaled copy.

Original Rectangle

12
10
Scaled Copy

5
10 ·
= 5
The scale factor is

Answer 1

To find the scale factor between the original rectangle and the scaled copy, you can use the corresponding side lengths.

You have:

• Original rectangle side: 10 units
• Scaled copy side: 5 units

The scale factor can be found using the formula:

\[ \text{Scale Factor} = \frac{\text{Length in scaled copy}}{\text{Length in original rectangle}} \]

Substituting in the values we have:

\[ \text{Scale Factor} = \frac{5}{10} = \frac{1}{2} = 0.5 \]

Thus, the scale factor is \(0.5\).

To confirm, you can apply this scale factor to the other side of the original rectangle:

• Original rectangle side: 12 units

Calculating the scaled side:

\[ \text{Scaled side} = 12 \times 0.5 = 6 \text{ units} \]

So, the sides of the scaled copy would be 5 units and 6 units, which corresponds correctly to the concept of being scaled.

The final answer is:

The scale factor is \(0.5\).