Let ABC be an equilateral triangle and AD perpendicular to BC, then AB2 + BC2 + CA2 = ?
A. 3AD2
B. 5AD2
C. 2AD2
D. 4AD2
Answer: Option D
Solution(By Examveda Team)
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
$$\left( {{{\text{a}}^2} - \frac{{{{\text{a}}^2}}}{4} = {\text{A}}{{\text{D}}^2}} \right)$$
Related Questions on Triangles
If ABC and PQR are similar triangles in which ∠A = 47° and ∠Q = 83°, then ∠C is:
A. 50°
B. 70°
C. 60°
D. 80°
In the following figure which of the following statements is true?
A. AB = BD
B. AC = CD
C. BC + CD
D. AD < Cd
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