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In triangle ABC, B = 90 degrees, AB = 25, and BC = 50.  If DBEF is a square, find the area of square DBEF.

 

 May 11, 2020
 #1
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We  have  two   similar  triangles  here....

 

Triangle  ADF  is similar to  triangle   ABC

 

And   this means  that

 

AD / DF  = AB /BC

 

AD/ DF   = 25 / 50

 

AD/ DF =  1/ 2

 

But  since  DBEF is a square.....then   BD = DF

 

So

 

AD / BD= 1/2  ⇒   AD : BD   =   1 : 2

 

Which means  that  BD   =  2/3   of  AB  =   (2/3)(25)

 

Then  the area of  DBEF = BD^2  =   [ (2/3) (25) ]^2 =  (4/9)(625)  = 2500/9  units^2

 

 

cool cool cool

 May 11, 2020

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