The area of an equilateral triangle with the equation of base as x+y-2=0 and the opposite vertex with the coordinates (2, -1) is sq. units.
The correct option is B12√3 Let 'p' be the length of the altitude i.e. the perpendicular distance from the point (2, -1) on the line x+y-2=0. ⇒p=(2−1−2√12+12∣∣∣=1√2Also,weknowthataltitudeofanequilateraltrianglewithsideais√3a2(∵Area=12×p×a=√3a24)⇒√3a2=1√2⇒a=√23⇒Area=√3a24=√34×23=12√3sq.units