The altitude of an equllateral triangle of side `2/(sqrt3)` cm is

Options

A. `4/3 m`
B. `4/(sqrt3)m`
C. `4/3 m`
D. `1 m`

Answer

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

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

**Step 1: Identify the side length of the triangle.**
The side length of the equilateral triangle is given as:
\[ \text{side} = \frac{2}{\sqrt{3}} \, \text{cm} \]

**Step 2: Substitute the side length into the altitude formula.**
Now, we will substitute the side length into the altitude formula:
\[ h = \frac{\sqrt{3}}{2} \times \frac{2}{\sqrt{3}} \]

**Step 3: Simplify the expression.**
Now, we simplify the expression:
\[ h = \frac{\sqrt{3} \times 2}{2 \times \sqrt{3}} \]
\[ h = \frac{2\sqrt{3}}{2\sqrt{3}} \]
\[ h = 1 \, \text{cm} \]

Thus, the altitude of the equilateral triangle is:
\[ \text{Altitude} = 1 \, \text{cm} \]

**Final Answer:**
The altitude of the equilateral triangle is 1 cm.

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