Height of equilateral triangle having side 6 cm, is :

Question

Accepted Answer

To find 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:

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

Substituting the given side length of 6 cm 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 of 6 cm is indeed $3\sqrt{3}$ cm.

2. **Option 2: 3 cm** - This option is incorrect because it does not account for the $\sqrt{3}$ factor that arises from the geometry of an equilateral triangle. The height is not simply half of the side length.

3. **Option 3: $\sqrt{3}$ cm** - This option is incorrect because it represents the height of an equilateral triangle with a side length of 2 cm, not 6 cm. The height must be scaled appropriately with the side length.

4. **Option 4: $9\sqrt{3}$ cm** - This option is incorrect because it overestimates the height. The factor of 9 suggests a miscalculation, as the correct factor is 3 when the side length is 6 cm.

In conclusion, the correct height of the equilateral triangle with a side length of 6 cm is $3\sqrt{3}$ cm, making Option 1 the correct choice.