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.

Answer

N/a

Explanation

Given that, equilateral `DeltaABC` having equation of base is `x+y=2`.
In `DeltaABD, sin60^@=(AD)/(AB)`
`rArr AD=AB sin 60^@=ABsqrt3/(2)`
`because AD =ABsqrt3/(2)`......(i)
Now the length of perpendicular from `(2,-1)` to the line `x+y=2` is given by `AD=|(2+(-1)-2)/(sqrt(1^2+1^2))|=(1)/sqrt(2)`
From Eq.(i) , `(1)/(sqrt2)=AB(sqrt3)/(2)AB=sqrt(2/3)`