In an equilateral triangle of side `3sqrt(3)` cm then length of the altitude is

Options

A. h = 4 cm
B. h = 5 cm
C. h = 4.5 cm
D. h = 5.5 cm

Answer

To find the length of the altitude (height) of an equilateral triangle with a given side length, we can use the formula for the altitude of an equilateral triangle:

### Step-by-Step Solution:

1. **Identify the side length of the triangle**:
Given that the side length \( A \) of the equilateral triangle is \( 3\sqrt{3} \) cm.

2. **Use the formula for the altitude**:
The formula for the altitude \( H \) of an equilateral triangle is given by:
\[ H = \frac{\sqrt{3}}{2} A \]

3. **Substitute the value of \( A \)**:
Substitute \( A = 3\sqrt{3} \) into the formula:
\[ H = \frac{\sqrt{3}}{2} \times (3\sqrt{3}) \]

4. **Simplify the expression**:
Calculate the multiplication:
\[ H = \frac{3 \cdot \sqrt{3} \cdot \sqrt{3}}{2} \]
Since \( \sqrt{3} \cdot \sqrt{3} = 3 \):
\[ H = \frac{3 \cdot 3}{2} = \frac{9}{2} \]

5. **Convert to decimal**:
Convert \( \frac{9}{2} \) to decimal form:
\[ H = 4.5 \text{ cm} \]

### Final Answer:
The length of the altitude of the equilateral triangle is \( 4.5 \) cm.