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In right triangle ABC shown in the diagram below, altitude BD isdrawn to hypotenuse AC, CD = 12, and AD = 3.
What is the length of AB?

 

 Mar 17, 2021
 #1
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Triangle ADB  is similar to triangle  BDC

 

So

 

AD  / DB =  DB / DC

 

3  / DB  =  DB  /  12       cross-multiply

 

12 * 3  = DB * DB

 

36  = DB^2

 

DB  = 6

 

AB = sqrt (DB^2  + AD^2)  =   sqrt  ( 6^2  + 3^2)    =  sqrt  ( 45)  =  sqrt (9 ) * sqrt (5)  = 3sqrt (5)

 

 

cool cool cool

 Mar 17, 2021

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