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Since triangle(ABC) is a right triangle, AC²  =  AB² + BC²   --->   AC²  =  5² + 3²   --->   AC²  =  34  

   --->   AC  =  sqrt(34)

 

To find BD, I'm going to find the area of triangle(ABC) in two ways.

 

First way  --  with base AB and height BC:  Area  =  ½·5·3  =  7.5

Second way  --  with base AC and height D:  7.5  =  ½·sqrt(34)·BD   --->   BD  =  15/sqrt(34)

 

Now, add these parts together ...