question_answer

ABC is a triangle right angled at A and a perpendicular AD is drawn on the hypotenuse BC. What is \[BC\cdot AD\]equal to?

A) \[AB\cdot AC\]                          

B) \[AB\cdot AD\]

C) \[CA\cdot CD\]                          

D) \[AD\cdot DB\]

Correct Answer: A

Solution :

ABC is a right angled triangle right angled at A. Also AD\[\bot \]BC \[\Delta \]ABC and \[\Delta \]DBA are similar \[\Rightarrow \,\,\,\,\,\,\frac{BC}{AB}=\frac{AC}{AD}\Rightarrow \]BC\[\cdot \]AD = AB\[\cdot \]AC