△ABC is an equilateral triangle in which D, E and F are the points on sides BC, AC and AB, respectively, such that AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Which of the following is true?
Answer & explanation
Correct answer: option 4
We know that,
Height of the equilateral triangle = \(\frac{\sqrt {3}}{2}\) × Side
Here,
Side = AB = BC = CA
Height = AD = BE = CF
\(\frac{\sqrt {3}}{2}\) × AC = BE
\(\sqrt {3}\) AC = 2BE
Squaring on both sides = 3 AC2 = 4 BE2