The equation of the base of an equilateral triangle is `x+y=2` and its vertex is `(2,-1)dot` Find the length and equations of its sides.

Explanation

To solve the problem step-by-step, we need to find the length of the sides and the equations of the sides of the equilateral triangle given the base equation and the vertex.

### Step 1: Identify the given information
- The equation of the base (line) of the equilateral triangle is \( x + y = 2 \).
- The vertex of the triangle is \( A(2, -1) \).

### Step 2: Find the distance from the vertex to the base
To find the length of the sides of the triangle, we first need to calculate the perpendicular distance from point \( A(2, -1) \) to the line \( x + y - 2 = 0 \).
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