The area of an equilateral triangle is 400 `sqrt3` sq.m. Its perimeter is:

Options

A. 120 m
B. 150 m
C. 90m
D. 135 m

Answer

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

### Step-by-Step Solution:

1. **Understand the formula for the area of an equilateral triangle**:
The area \( A \) of an equilateral triangle with side length \( a \) is given by the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

2. **Set up the equation with the given area**:
We know from the problem that the area is \( 400 \sqrt{3} \) sq.m. Therefore, we can set up the equation:
\[ 400 \sqrt{3} = \frac{\sqrt{3}}{4} a^2 \]

3. **Eliminate \( \sqrt{3} \) from both sides**:
To simplify the equation, we can divide both sides by \( \sqrt{3} \):
\[ 400 = \frac{1}{4} a^2 \]

4. **Multiply both sides by 4**:
To solve for \( a^2 \), multiply both sides of the equation by 4:
\[ 1600 = a^2 \]

5. **Take the square root of both sides**:
Now, take the square root to find \( a \):
\[ a = \sqrt{1600} = 40 \text{ m} \]

6. **Calculate the perimeter**:
The perimeter \( P \) of an equilateral triangle is given by:
\[ P = 3a \]
Substituting the value of \( a \):
\[ P = 3 \times 40 = 120 \text{ m} \]

### Final Answer:
The perimeter of the equilateral triangle is \( 120 \) meters.