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

Options

A. `sqrt(20/3)`
B. `2/sqrt15`
C. `sqrt8/15`
D. `sqrt15/2`

Answer

A

Explanation

` therefore |AD| = | (-2-2-1)/(sqrt((2)^(2) + (-1)^(2)))|= |(-5)/sqrt5| = sqrt5`
` (##ARH_EGN_PRG_MAT_C04_E02_029_S01.png" width="80%">
` and " in " Delta ABD, tan 60^(@) = (AD)/(BD)`
` Rightarrow sqrt3 = (sqrt5)/(BD) Rightarrow BD = sqrt(5/3)`
` BC= 2BD= 2 sqrt(5/3) = sqrt(20/3)`