The altitude of an equilateral triangle of side `2sqrt3` cm is -----

Options

A. `sqrt3/2` cm
B. 1/2 cm
C. `sqrt3/4 `cm
D. 3 cm

Answer

To find the altitude of an equilateral triangle with a side length of \(2\sqrt{3}\) cm, we can use the formula for the altitude (height) of an equilateral triangle:

\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times \text{side} \]

**Step 1: Identify the side length of the triangle.**
The side length of the equilateral triangle is given as \(2\sqrt{3}\) cm.

**Step 2: Substitute the side length into the altitude formula.**
Using the formula for the altitude:
\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times (2\sqrt{3}) \]

**Step 3: Simplify the expression.**
Now, we can simplify the expression:
\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times 2\sqrt{3} = \sqrt{3} \times \sqrt{3} = 3 \text{ cm} \]

Thus, the altitude of the equilateral triangle is \(3\) cm.

### Summary of the Solution:
The altitude of an equilateral triangle with side length \(2\sqrt{3}\) cm is \(3\) cm.

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