Quantitative Aptitude Ques 2068

Question: ABC is a triangle right angled at A and a perpendicular AD is drawn on the hypotenuse BC. The value of $ BC\cdot AD $ is equal to

Options:

A) $ AB\cdot AC $

B) $ AB\cdot AD $

C) $ CA\cdot CD $

D) $ AD\cdot DB $

Show Answer

Answer:

Correct Answer: A

Solution:

  • In case of a right angled triangle, if we draw a perpendicular from the vertex containing right angle to the hypotenuse, we get three triangles, two smaller and one original and these three triangles are similar triangles.
    So, $ \Delta ABC\sim \Delta DBA\sim \Delta DAC $ $ \frac{BC}{AB}=\frac{AC}{AD} $

$ \therefore $ $ BC\cdot AD=AB\cdot AC $

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