Question
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
$$\left( {{{\text{a}}^2} - \frac{{{{\text{a}}^2}}}{4} = {\text{A}}{{\text{D}}^2}} \right)$$
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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
$$\left( {{{\text{a}}^2} - \frac{{{{\text{a}}^2}}}{4} = {\text{A}}{{\text{D}}^2}} \right)$$
Was this answer helpful ?
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