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What does BD equal to?​

 

 Mar 31, 2021
 #1
avatar+149 
+1

\(CA=\sqrt{20^2+16^2}=\sqrt{656}\)

\(BD^2+20^2=BA^2\)

\(AC^2+BA^2=(DC+BD)^2\) =>\(656+(BD^2+20^2)=(16+BD)^2\)

\(656+BD^2+400=256+32BD+BD^2\)

\(1056-256=800=32BD\)

\(BD=25\)

 Mar 31, 2021
 #2
avatar+121004 
+1

Thanks, James

 

Another  method

 

We  have  the relationship that

 

BD / AD  = AD  /  DC

 

BD / 20  =  20 / 16           cross-multiply

 

16 BD  =  20 * 20

 

16 BD  =  400

 

BD  =  400  /16     =   25

 

 

cool cool cool

 Mar 31, 2021
 #3
avatar+1450 
+2

BD = 20(20 / 16) laugh

 Mar 31, 2021

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