Q13 of 59 Page 178

If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.


Let Δ ABC be an equilateral triangle.


Given: Equation of the base BC is x + y = 2


We know that, in an equilateral triangle all angles are of 60°


So, in Δ ABD





We know that,


the distance d of a point P(x0, y0) from the line Ax + By + C = 0 is given by



Now, length of perpendicular from vertex A(2, -1) to the line x + y = 2 is





Squaring both the sides, we get






Hence, the required length of side is


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