If the equation of base of an equilateral triangle is `2x-y=1` and the vertex is `(-1,2),` then the length of the sides of the triangle is (a)`sqrt((20)/3)` (b) `2/(sqrt(15))` (c)`sqrt(8/(15))` (d) `sqrt((15)/2)`

Options

A. `sqrt(20//3)`
B. `2//sqrt(15)`
C. `sqrt(8//15)`
D. `sqrt(15//2)`

Answer

A

Explanation

`AD =|(-2-2-1)/(sqrt((2)^(2)+(-1)^(2)))| =|(-5)/(sqrt(5))| = sqrt(5)`
`therefore " tan" 60^(@) = (AD)/(BD)`
`"or " sqrt(3) = (sqrt(5))/(BD)`
`"or " BD = sqrt((5)/(3))`
`therefore BC=2BD = 2 sqrt((5)/(3)) = sqrt((20)/(3))`