Quantitative Aptitude Ques 668

Question: In an equilateral $ \Delta ABC, $ if $ AD\bot BC, $ then which of the following is true?

Options:

A) $ 2AB^{2}=3AD^{2} $

B) $ 4AB^{2}=3AD^{2} $

C) $ 3AB^{2}=4AD^{2} $

D) $ 3AB^{2}=2AD^{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ AB=BC=CA $ $ AD\bot BC $
    $ \Rightarrow $ $ BD=DC $ In $ \Delta ABD, $ $ AB^{2}=BD^{2}+AD^{2} $

$ \Rightarrow $ $ AB^{2}={{( \frac{1}{2}AB )}^{2}}+AD^{2} $

$ \Rightarrow $ $ AB^{2}-\frac{1}{4}AB^{2}=AD^{2} $
$ \Rightarrow $ $ 3AB^{2}=4AD^{2} $

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