The equation of the base of an equilateral triangle is x + y = 2 and one vertex is ( 2 , - 1 ) , then the length of the side of the triangle is

Step-by-step solution

Let, ∆ A B C , be the triangle, with side B C as x + y = 2 , and vertex A as 2 ,   - 1 . The length of perpendicular from the point x 1 ,   y 1 to the line a x + b y + c = 0 is a x 1 + b y 1 + c a 2 + b 2 . Hence, the length of altitude A M = 2 - 1 - 2 1 2 + 1 2 ⇒ A M = 1 2 . We know that, in an equilateral triangle, altitude, median, angle bisector all are same. Hence, A M is also the median, thus M C = 1 2 B C = 1 2 A C . Now, in ∆ A M C , by Pythagoras theorem A C 2 =   A M 2 + M