Question

The rectangles below are scaled copies of one another. The side that corresponds to 8 units in the original rectangle is 4 units in the scaled copy.
Start by finding the scale factor from the original rectangle to the scaled copy.
Original Rectangle

8
4
Scaled Copy

4
The scale factor is
1
2
.
Great job!
The scale factor is
2
1
​
. Now, find the missing side length of the scaled copy.
Original Rectangle

8
4
Scaled Copy

4
8 ·
2
1
​
= 4
The scale factor is
2
1
​
.

Answer 1

To find the missing side length of the scaled copy, you've already determined the scale factor from the original rectangle to the scaled copy is \( \frac{1}{2} \).

You can confirm this by looking at how the corresponding sides relate:

- For the original rectangle, one side measures 8 units, and the corresponding (scaled) side measures 4 units. Thus, the scale factor can be found using:

\[
\text{Scale factor} = \frac{\text{length of scaled copy}}{\text{length of original}} = \frac{4}{8} = \frac{1}{2}
\]

Now, to find the missing side length in the scaled copy corresponding to the original rectangle's side of 4 units, we can apply the scale factor:

\[
\text{Missing side length in scaled copy} = \text{length of original} \times \text{scale factor} = 4 \times \frac{1}{2} = 2 \text{ units}
\]

So, the missing side length of the scaled copy is **2 units**.