The perimeter of an equilateral triangle is 60m. The area is

Options

A. `10sqrt(3)m^(2)`
B. `15sqrt(3)m^(2)`
C. `20sqrt(3)m^(2)`
D. `100sqrt(3)m^(2)`

Answer

To find the area of an equilateral triangle given its perimeter, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
- The perimeter of the equilateral triangle is given as 60 meters.

2. **Determine the length of one side**:
- Since it is an equilateral triangle, all three sides are equal. Let the length of one side be \( A \).
- The formula for the perimeter \( P \) of an equilateral triangle is:
\[ P = 3A \]
- Setting this equal to the given perimeter:
\[ 3A = 60 \]
- To find \( A \), divide both sides by 3:
\[ A = \frac{60}{3} = 20 \text{ meters} \]

3. **Use the formula for the area of an equilateral triangle**:
- The area \( A_t \) of an equilateral triangle can be calculated using the formula:
\[ A_t = \frac{\sqrt{3}}{4} A^2 \]
- Substitute \( A = 20 \) into the formula:
\[ A_t = \frac{\sqrt{3}}{4} \times (20)^2 \]

4. **Calculate \( A^2 \)**:
- Calculate \( 20^2 \):
\[ 20^2 = 400 \]

5. **Substitute \( A^2 \) back into the area formula**:
- Now substitute \( 400 \) into the area formula:
\[ A_t = \frac{\sqrt{3}}{4} \times 400 \]

6. **Simplify the area**:
- Calculate \( \frac{400}{4} \):
\[ \frac{400}{4} = 100 \]
- Therefore, the area is:
\[ A_t = 100\sqrt{3} \text{ square meters} \]

### Final Answer:
The area of the equilateral triangle is \( 100\sqrt{3} \) square meters.

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