Quantitative Aptitude Ques 1127
Question: In a right angled triangle, the product of two sides is equal to half of the square of the third side, i.e. hypotenuse. One of the acute angles must be
Options:
A) $ 60{}^\circ $
B) $ 30{}^\circ $
C) $ 45{}^\circ $
D) $ 15{}^\circ $
Show Answer
Answer:
Correct Answer: C
Solution:
- According to the question, $ AB\cdot BC=\frac{1}{2}\cdot AC^{2} $
$ \Rightarrow $ $ 2AB\cdot BC=AC^{2} $
$ \Rightarrow $ $ 2AB\cdot BC=AB^{2}+BC^{2} $
$ \Rightarrow $ $ AB^{2}+BC^{2}-2AB\cdot BC=0 $
$ \Rightarrow $ $ {{(AB-BC)}^{2}}=0 $
$ \Rightarrow $ $ AB=BC $
$ \therefore $ $ \angle BAC=\angle BCA=45{}^\circ $
BETA
