A park has a triangular pond. The area of the pond is 720 square meters. In a scale drawing of the park, 1 centimeter=15 meters. If the height of the pond is 3 centimeters in the scale drawing, what is the base of the pond in the scale drawing

To solve this problem, we will use the relationship between the area of a triangle, the scale factor, and the given dimensions in the scale drawing.

### Steps:

1. **Understand the relationship between area, base, and height**:
   - The area \( A \) of a triangle is given by the formula:
     \[
     A = \frac{1}{2} \times \text{base} \times \text{height}
     \]
   - Here, the actual area of the pond is 720 square meters.

2. **Convert the height from the scale drawing to the actual height**:
   - The height in the drawing is 3 centimeters.
   - Using the scale \( 1 \, \text{cm} = 15 \, \text{m} \):
     \[
     \text{Actual height} = 3 \, \text{cm} \times 15 \, \text{m/cm} = 45 \, \text{meters}
     \]

3. **Find the actual base of the pond**:
   - Rearrange the area formula to solve for the base:
     \[
     \text{base} = \frac{2 \times \text{Area}}{\text{height}} = \frac{2 \times 720 \, \text{m}^2}{45 \, \text{meters}} = \frac{1440 \, \text{m}^2}{45 \, \text{meters}} = 32 \, \text{meters}
     \]

4. **Convert the actual base to the scale drawing base**:
   - Using the scale \( 1 \, \text{cm} = 15 \, \text{m} \):
     \[
     \text{Base in drawing} = \frac{32 \, \text{meters}}{15 \, \text{m/cm}} \approx 2.13 \, \text{cm}
     \]

So, the base of the pond in the scale drawing is approximately **2.13 centimeters**.

Would you like more details or have any questions?

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Here are some related questions you might find interesting:

1. What would the area of the pond be in the scale drawing?
2. If the scale was 1 cm = 20 meters, what would the base be in the drawing?
3. How would the base change if the height in the drawing was 4 centimeters?
4. What is the perimeter of the triangular pond in the actual park?
5. If the base was 5 centimeters in the drawing, what would the actual base be?

**Tip:** When dealing with areas in scaled drawings, remember to convert all linear dimensions before using them in area-related formulas.

Learn how to calculate the base of a triangular pond in a scale drawing. Given the area of the pond (720 square meters), the scale factor (1 cm = 15 meters), and the height in the scale drawing (3 centimeters), find the base in centimeters. Includes step-by-step solution and formula application.

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