(35) Analyze Raul planned a painting of his mountain cabls 20 ft tall and the trees around it are 30 ft tall. The height of the cabin in his painting will be 6 inches. a. What is the scale from the actual cabin to the painting? b. How tall should Raul paint the trees?

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Let's analyze Raul's painting project step by step.

### Given:
- **Actual height of the cabin:** 20 feet
- **Actual height of the trees:** 30 feet
- **Height of the cabin in the painting:** 6 inches

---

### **a. Determining the Scale**

**Step 1:** Convert the actual height of the cabin from feet to inches to match the painting's unit.

$$
20 \text{ feet} \times 12 \text{ inches/foot} = 240 \text{ inches}
$$

**Step 2:** Establish the scale by comparing the actual height to the painting height.

$$
\text{Scale} = \frac{\text{Actual Height}}{\text{Painting Height}} = \frac{240 \text{ inches}}{6 \text{ inches}} = 40
$$

**Step 3:** Express the scale in the standard ratio format.

$$
\text{Scale} = 1:40
$$

*This means **1 inch** on the painting represents **40 inches** in reality.*

---

### **b. Calculating the Height of the Trees in the Painting**

**Step 1:** Convert the actual height of the trees to inches.

$$
30 \text{ feet} \times 12 \text{ inches/foot} = 360 \text{ inches}
$$

**Step 2:** Apply the established scale to find the painting height.

$$
\text{Painting Height of Trees} = \frac{\text{Actual Height of Trees}}{\text{Scale}} = \frac{360 \text{ inches}}{40} = 9 \text{ inches}
$$

**Conclusion:**
- **a.** The scale is **1:40**.
- **b.** Raul should paint the trees **9 inches** tall.

---

**Summary:**

a. The scale is 1 to 40.

b. The trees should be painted 9 inches tall.
a. The scale is 1:40. b. Raul should paint the trees 9 inches tall.

(35) Analyze Raul planned a painting of his mountain cabls 20 ft tall and the trees around it are 30 ft tall. The height of the cabin in his painting will be 6 inches. a. What is the scale from the actual cabin to the painting? b. How tall should Raul paint the trees?

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