The area of an equilateral triangle is `400sqrt(3)` sq.m. Its perimeter is :

Options

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

Answer

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

### Step 1: Use 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:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

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

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

### Step 4: Multiply both sides by 4.
To isolate \( a^2 \), multiply both sides by 4:
\[ a^2 = 1600 \]

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

### Step 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.

---