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In rectangle ABCD, corner A is folded over crease DE to point F on BC.  Find BC.

 

 Apr 21, 2022
 #1
avatar+122387 
+1

A little hard to visualize this   (I did it with a piece of paper   - hope I didn't mess it up  !!!)

 

When we make the fold  EF = EA  = 9  and  EB = 6

 

And triangle EBF is right  so    BF  = sqrt  [ 9^2 - 6^2 ]  = sqrt  45  =  3sqrt 5

 

And FD =  BC

 

And triangle FDC is right  with   DC = 9    FC  = BC - BF =   BC - 3sqrt5  = BC - sqrt 45

 

So

 

FC =  sqrt  [ FD^2 -  DC^2 ]

 

(BC - sqrt 45)  =  sqrt  [ BC^2  - 81) 

 

(BC - sqrt 45)^2   = BC^2 - 81

 

BC^2 - 2*BC*sqrt45 + 45  = BC^2 - 81

 

-2sqrt (45) BC =  -81 -  45

 

-2 sqrt (45) BC =  -126

 

BC  =    126 / ( 2 sqrt 45)  =   126 / (2 * 3 * sqrt 5)  =   21 / sqrt 5  =  (21/5)sqrt 5

 

 

cool cool cool

 Apr 21, 2022
 #2
avatar+125 
-3

Chris is gonna help you on this

 Apr 21, 2022

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