If the length of a side of an equilateral triangle is 6 cm, then its height is :

Question

Accepted Answer

To determine the height of an equilateral triangle with a side length of 6 cm, we can use the formula for the height of an equilateral triangle:

$$ \text{Height} = \frac{\sqrt{3}}{2} \times \text{side length} $$

Given that the side length is 6 cm, we substitute this value into the formula:

$$ \text{Height} = \frac{\sqrt{3}}{2} \times 6 $$

$$ \text{Height} = 3\sqrt{3} \, \text{cm} $$

Therefore, the height of the equilateral triangle is $3\sqrt{3}$ cm, which corresponds to Option 1.

**Explanation for why each option is correct or incorrect:**

1. **Option 1: $3\sqrt{3}$ cm**  
   This is the correct answer. The calculation above shows that the height of the equilateral triangle with a side length of 6 cm is indeed $3\sqrt{3}$ cm.

2. **Option 2: $9\sqrt{3}$ cm**  
   This option is incorrect. The formula for the height of an equilateral triangle does not yield $9\sqrt{3}$ cm when the side length is 6 cm. The calculation clearly shows that the height is $3\sqrt{3}$ cm.

3. **Option 3: 3 cm**  
   This option is incorrect. The height of an equilateral triangle is not simply the side length divided by 2 or any other simple fraction without the $\sqrt{3}$ factor. The correct height involves multiplying by $\frac{\sqrt{3}}{2}$, resulting in $3\sqrt{3}$ cm, not 3 cm.

4. **Option 4: $5\sqrt{3}$ cm**  
   This option is incorrect. The calculation for the height of an equilateral triangle with a side length of 6 cm does not result in $5\sqrt{3}$ cm. The correct height is $3\sqrt{3}$ cm, as derived from the formula.

In conclusion, the correct height of the equilateral triangle is $3\sqrt{3}$ cm, making Option 1 the correct choice.