question_answer

If ABC is an equilateral triangle and D is a point on BC such that \[AD\bot BC,\] then

A) AB : BD = 1 : 1

B) AB : BD = 1 : 2

C) AB : BD = 2 : 1

D) AB : BD = 3 : 2

Correct Answer: C

Solution :

[c] \[\because \]\[\Delta ABC\]is equilateral and \[AD\bot BC.\] \[\therefore \]      \[BD=DC=\frac{1}{4}\,BC\] Now, \[AB:BD=AB:\frac{1}{2}\] \[BC=1:\frac{1}{2}\]     \[(\because AB=AC)\] \[AB:BD=2:1\]