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ABC is a triangle,right angled at B,D is a point on AC such that ABD=45. If AC=6 and AD=2,then legth of AB is?

ABC is a triangle,right angled at B,D is a point on AC such that ABD=45. If AC=6 and AD=2,then legth of AB is?
 

Grade:12

1 Answers

mycroft holmes
272 Points
7 years ago
BD is the angular bisector and so by the property of angular bisector we have
 
AD/CD = AB/BC. From the given info its clear that AD/CD = ½.
 
Hence if AB = x, then BC = 2x. Now use Pythagoras to obtain x = \frac{6\sqrt 5}{5}

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