https://file.aiquickdraw.com/mathbot/file/1725751147768158zggj7.jpg

Let's break down the math problems from the image you've uploaded. The problems deal with using scales to find distances. I'll interpret the equations and provide detailed solutions.

### Problem 1:
**Given:**
Tasha makes a scale drawing of points of interest between two parks. The drawing uses a scale of 2 cm = 6 meters. 

In her drawing:
- The distance between the parks is 12 cm.

**To find:**
The actual distance between the parks.

**Solution:**
The scale is \( 2 \, \text{cm} = 6 \, \text{m} \). Therefore:
\[
\frac{2 \, \text{cm}}{6 \, \text{m}} = \frac{12 \, \text{cm}}{x \, \text{m}}
\]
Cross-multiply:
\[
2x = 12 \times 6 = 72
\]
Solve for \( x \):
\[
x = \frac{72}{2} = 36 \, \text{m}
\]
**Answer:** The actual distance is **36 meters**.

---

### Problem 2:
**Given:**
Robert is building a scale model of a shelf. The actual shelf is 6 feet tall, and his model will be \( \frac{1}{12} \) of the actual size. 

**To find:**
- The height of the model.
- Whether it fits in a space that is 6 inches tall.

**Solution:**
First, convert the actual height of the shelf to inches:
\[
6 \, \text{ft} = 6 \times 12 = 72 \, \text{inches}
\]
Now, use the scale \( \frac{1}{12} \):
\[
\text{Model height} = \frac{1}{12} \times 72 = 6 \, \text{inches}
\]
Since the model is 6 inches tall, it **will not fit** in a space that is also 6 inches tall, as there would be no clearance.

**Answer:** The model height is **6 inches**, and it **will not fit** in the 6-inch tall space.

---

### Problem 3:
**Given:**
Amber is making a scale drawing of a movie screen. The actual dimensions of the screen are 20 feet tall and 60 feet wide. The width of the screen in the drawing is 9 cm.

**To find:**
The height of the screen in the drawing.

**Solution:**
We have the following proportions based on the actual width and height:
\[
\frac{60 \, \text{ft}}{9 \, \text{cm}} = \frac{20 \, \text{ft}}{x \, \text{cm}}
\]
Cross-multiply:
\[
60x = 9 \times 20 = 180
\]
Solve for \( x \):
\[
x = \frac{180}{60} = 3 \, \text{cm}
\]
**Answer:** The height of the screen in the drawing is **3 cm**.

---

### Summary of Answers:
1. The actual distance between the parks is **36 meters**.
2. The model height is **6 inches**, and it **will not fit** in the space.
3. The height of the screen in the drawing is **3 cm**.

Would you like any further details or explanations?

### Here are 5 related questions to expand your knowledge:
1. How would the result change in problem 1 if the drawing distance were 15 cm?
2. If Robert wanted his shelf model to fit, what would the scale factor need to be?
3. How can you convert different units (e.g., feet to meters) when using scales?
4. What happens if Amber increases the width of her drawing? How would that affect the height?
5. Can you solve similar problems involving different scale ratios?

### Tip:
When solving scale problems, always keep the units consistent (e.g., convert feet to inches or vice versa) before applying the proportion to avoid calculation errors.

Learn how to solve scale drawing problems using proportions and unit conversions. This solution covers key concepts like cross-multiplication and scaling to determine actual distances and dimensions. Suitable for Grades 5-7.

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