If the circumradius of an equilateral triangle ABC be 8 cm, then the height of the triangle is

Options

A. 16 cm
B. 6 cm
C. 8 cm
D. 12 cm

Answer

To find the height of an equilateral triangle given its circumradius, we can use the relationship between the circumradius (R) and the height (h) of the triangle.

### Step-by-Step Solution:

1. **Understand the Relationship**: For an equilateral triangle, the circumradius (R) is related to the height (h) by the formula:
\[ R = \frac{2}{3} h \]

2. **Substitute the Given Value**: We are given that the circumradius \( R = 8 \) cm. We can substitute this value into the formula:
\[ 8 = \frac{2}{3} h \]

3. **Isolate h**: To find h, we need to isolate it. We can do this by multiplying both sides of the equation by \( \frac{3}{2} \):
\[ h = 8 \times \frac{3}{2} \]

4. **Calculate h**: Now, we perform the multiplication:
\[ h = 8 \times \frac{3}{2} = \frac{24}{2} = 12 \text{ cm} \]

5. **Conclusion**: The height of the equilateral triangle is \( 12 \) cm.

### Final Answer:
The height of the triangle is \( 12 \) cm.