SATHEE: Quantitative Aptitude Ques 1127

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 $

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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:

Answer:

Solution:

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