The area of an equilateral triangle is `49sqrt(3) cm^(2)`. Find its side (in cm).

Options

A. 7
B. 14
C. 28
D. 42

Answer

To find the side of an equilateral triangle given its area, we can use the formula for the area of an equilateral triangle:

\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]

where \( a \) is the length of a side of the triangle.

### Step 1: Set up the equation
We know the area of the triangle is given as \( 49\sqrt{3} \, \text{cm}^2 \). Therefore, we can set up the equation:

\[ \frac{\sqrt{3}}{4} a^2 = 49\sqrt{3} \]

### Step 2: Eliminate \(\sqrt{3}\)
To simplify the equation, we can divide both sides by \(\sqrt{3}\):

\[ \frac{1}{4} a^2 = 49 \]

### Step 3: Multiply by 4
Next, we can multiply both sides by 4 to isolate \( a^2 \):

\[ a^2 = 49 \times 4 \]

### Step 4: Calculate \( 49 \times 4 \)
Now, we calculate \( 49 \times 4 \):

\[ a^2 = 196 \]

### Step 5: Take the square root
To find \( a \), we take the square root of both sides:

\[ a = \sqrt{196} \]

### Step 6: Calculate the square root
Calculating the square root gives us:

\[ a = 14 \, \text{cm} \]

### Final Answer
Thus, the side of the equilateral triangle is \( 14 \, \text{cm} \).

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