Question

Equation of the base of an equilateral triangle x + y is equal to 2

Answer 1

Let a be the length of each side of the equilateral triangle.

The length of the perpendicular p from (2,-1) on x+y−2=0

⇒p=|2−1−2√12+12|

Now
Consider the Δ ABD

sin60∘=pa

⇒√3/2=1/√2a

⇒a=2/√3×1/√2

a=√2/3

hence the length of the side of the equilateral triangle is √2/3