The 1.80 m tall lady makes a 9 m long shadow, and the palm tree makes 26 m long shadow. Find the height of the tree. [Draw a diagram by yourself]

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UpStudy AI · Accepted Answer

To determine the height of the palm tree, we can use the concept of **similar triangles**. When two objects cast shadows under the same lighting conditions (like the sun), the ratios of their heights to the lengths of their shadows are equal.

### Given:
- **Lady's height:** 1.80 meters
- **Lady's shadow length:** 9 meters
- **Palm tree's shadow length:** 26 meters
- **Palm tree's height:** $$ h $$ meters (unknown)

### Step-by-Step Solution:

1. **Set Up the Proportion:**
   
   The ratio of the lady's height to her shadow is equal to the ratio of the palm tree's height to its shadow.

$$
   \frac{\text{Lady's Height}}{\text{Lady's Shadow}} = \frac{\text{Tree's Height}}{\text{Tree's Shadow}}
   $$

Substituting the known values:

$$
   \frac{1.80 \, \text{m}}{9 \, \text{m}} = \frac{h}{26 \, \text{m}}
   $$

2. **Solve for $$ h $$:**

$$
   \frac{1.80}{9} = \frac{h}{26}
   $$

$$
   \frac{1.80}{9} = 0.2
   $$

$$
   0.2 = \frac{h}{26}
   $$

Multiply both sides by 26 to isolate $$ h $$:

$$
   h = 0.2 \times 26 = 5.2 \, \text{meters}
   $$

### Conclusion:

The height of the palm tree is **5.2 meters**.

### Diagram Illustration:

While I can't draw a diagram here, imagine two similar triangles:

1. **First Triangle (Lady):**
   - **Height:** 1.80 m
   - **Shadow:** 9 m

2. **Second Triangle (Palm Tree):**
   - **Height:** $$ h $$ meters
   - **Shadow:** 26 m

Since the triangles are similar, their corresponding sides are proportional, leading to the solution above.

**Answer:**  
The palm tree is 5.2 meters tall.
The palm tree is 5.2 meters tall.

The 1.80 m tall lady makes a 9 m long shadow, and the palm tree makes 26 m long shadow. Find the height of the tree. [Draw a diagram by yourself]

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