Let ABC be an equilateral triangle and AD perpendicular to BC, then AB2 + BC2 + CA2 = ?

Answer: Option D

AB² = AD² + BD² . . . . . . . (i)
AC² = AD² + CD² . . . . . . . (ii)
AB² + AC² = 2AD² + BD² + CD²
AB² + AC² + BC² = 2AD² + a² + $$\frac{{\text{a}}^2}{4}$$ + $$\frac{{\text{a}}^2}{4}$$
AB² + AC² + BC² = 4AD²
          $$\left({\text{a}}^2-\frac{{\text{a}}^2}{4}=\text{A}{\text{D}}^2\right)$$