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In the figure shown, $AC=13$ and $DC=2$ units. What is the length of the segment $BD$? Express your answer in simplest radical form. 

Guest Nov 4, 2018
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We have this relationship

Angle DAB  = Angle CBD

Angle ADB = Angle CDB

So...by AA congruency......Triangle ADB  is similar to Triangle BDC

And AD  = AC - DC  = 13 - 2   = 11

So

AD / DB = BD / DC

 

So

 

AD * DC  =  BD^2

11 * 2  =  BD^2

BD^2 = 22

BD =  sqrt (22)

 

 

cool cool cool

CPhill  Nov 5, 2018

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