The area of an equilateral triangle is 173 then find the perimeter the equilateral triangle (use ` sqrt(3 ) = 1.73 )` is :

Options

A. 40 cm
B. 60 cm
C. 100 cm
D. 20 cm

Answer

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

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

### Step 2: Set up the equation with the given area.
We know the area of the triangle is 173. Therefore, we can set up the equation:
\[ \frac{\sqrt{3}}{4} x^2 = 173 \]

### Step 3: Substitute the value of \( \sqrt{3} \).
Given that \( \sqrt{3} = 1.73 \), we substitute this into the equation:
\[ \frac{1.73}{4} x^2 = 173 \]

### Step 4: Multiply both sides by 4 to eliminate the fraction.
\[ 1.73 x^2 = 173 \times 4 \]
Calculating the right side:
\[ 1.73 x^2 = 692 \]

### Step 5: Solve for \( x^2 \).
Now, divide both sides by 1.73:
\[ x^2 = \frac{692}{1.73} \]

### Step 6: Calculate \( x^2 \).
Performing the division:
\[ x^2 \approx 400 \]

### Step 7: Take the square root to find \( x \).
\[ x = \sqrt{400} = 20 \]

### Step 8: Calculate the perimeter of the triangle.
The perimeter \( P \) of an equilateral triangle is given by:
\[ P = 3x \]
Substituting the value of \( x \):
\[ P = 3 \times 20 = 60 \]

### Final Answer:
The perimeter of the equilateral triangle is \( 60 \) centimeters.

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