In an equilateral triangle, the lengths of the median is `sqrt3`cm, then find the length of the side of this equilateral triangle

Answer

To find the length of the side of an equilateral triangle given that the length of the median is \(\sqrt{3}\) cm, we can follow these steps:

### Step 1: Understand the properties of the equilateral triangle
In an equilateral triangle, all sides are equal, and the median from any vertex to the opposite side divides the triangle into two right triangles.

### Step 2: Label the triangle
Let the equilateral triangle be \(ABC\) with sides \(AB = AC = BC = a\). Let \(D\) be the midpoint of side \(BC\). The median \(AD\) is given as \(\sqrt{3}\) cm.

### Step 3: Use the properties of the median
The length of the median \(AD\) in an equilateral triangle can be calculated using the formula:
\[ AD = \frac{\sqrt{3}}{2} a \]
where \(a\) is the length of the side of the triangle.

### Step 4: Set up the equation
Since we know \(AD = \sqrt{3}\), we can set up the equation:
\[ \frac{\sqrt{3}}{2} a = \sqrt{3} \]

### Step 5: Solve for \(a\)
To isolate \(a\), multiply both sides of the equation by \(2\):
\[ \sqrt{3} a = 2\sqrt{3} \]
Now, divide both sides by \(\sqrt{3}\):
\[ a = 2 \]

### Conclusion
The length of the side of the equilateral triangle is \(2\) cm.