https://file.aiquickdraw.com/mathbot/file/1725750406519vtvpq896.jpg

Let's go over the two problems shown in the image.

### Problem 4:
"A rectangle has a length of 12 in. and a width of 8 in. Lexi makes a scale drawing of the rectangle using a scale factor of \( \frac{2}{3} \). What are the dimensions of the scale drawing?"

#### Solution:
To solve this, multiply both the length and width by the scale factor \( \frac{2}{3} \).

- Scale length: \( 12 \, \text{in} \times \frac{2}{3} = 8 \, \text{in} \)
- Scale width: \( 8 \, \text{in} \times \frac{2}{3} = 5.33 \, \text{in} \)

Thus, the dimensions of the scaled rectangle are:
- Length = 8 inches
- Width = 5.33 inches

---

### Problem 5:
"Emily works at a horse camp and makes a scale drawing of the barn. The actual width of a stable in her drawing is 15 in., and the length is 18 in. The actual width of the stable is 10 ft. What is the actual length of the stable?"

#### Solution:
We need to find the actual length of the stable. We know the actual width and can set up a proportion based on the width and length of the drawing.

- Drawing width: 15 in.
- Drawing length: 18 in.
- Actual width: 10 ft.

We can set up the proportion:
\[
\frac{\text{Drawing width}}{\text{Actual width}} = \frac{\text{Drawing length}}{\text{Actual length}}
\]
\[
\frac{15}{10} = \frac{18}{x}
\]

Now, solve for \( x \) (the actual length):

\[
15x = 180 \quad \text{(cross-multiply)}
\]
\[
x = \frac{180}{15} = 12 \, \text{ft}
\]

So, the actual length of the stable is 12 feet.

---

Do you have any questions about these solutions or need more details?

### Follow-up Questions:
1. What is the process to solve for dimensions using a scale factor?
2. How do you set up proportions in similar geometric figures?
3. Why do we need to use the same units when setting up proportions?
4. What happens if the scale factor is greater than 1?
5. Can you solve a scale factor problem if only one dimension is given?

**Tip:** When using proportions to solve problems, always ensure units match on both sides of the equation.

A rectangle has a length of 12 in. and a width of 8 in. Lexi makes a scale drawing of the rectangle using a scale factor of 2/3. What are the dimensions of the scale drawing? Emily works at a horse camp and makes a scale drawing of the barn. The actual width of a stable in her drawing is 15 in., and the length is 18 in. The actual width of the stable is 10 ft. What is the actual length of the stable?

Learn how to use scale factors to find dimensions in scaled rectangles and barns. Solve problems like scaling a 12x8 inch rectangle with a scale factor of 2/3 and using proportions to find the actual length of a stable. Perfect for students in Grades 6-8.

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