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ABC has a right angle at B. AC = 60, AE = 52 and CD = 39.  Find the length of DE.

 

 Dec 25, 2019
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Strictly by  "educated guessing"

 

Let us assume that  right triangle ABC  is a Pythagorean multiple  of a 3 - 4 - 5    right triangle  such that

BC = 36

AB = 48

AC  = 60

 

And let us assume that  right triangle  DBC  is  a Pythagorean multiple  of  a  5 -12- 13  right triangle  such that

DB = 15

BC = 36

DC = 39

 

 

Then BE  =  √ [AE^2 - AB^2]  =  √  [ 52^2  - 48^2]  = √400  =   20

 

So

 

DE = √[ DB^2  +  BE^2  ]  =  √ [ 15^2  + 20^2 ]  = √ 625   =  25

 

Here is the image to show  that this is true  :

 

 

 

cool cool cool

 Dec 27, 2019
edited by CPhill  Dec 27, 2019

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