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} $
BETA
