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Square $BCFE$ is inscribed in right triangle $AGD$, as shown below. If $AB = 28$ units and $CD = 58$ units, what is the area of square $BCFE$?

 Nov 5, 2018
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Angle EAB  = Angle CFD

Angle ABE  = Angle FCD

So, by AA congruency, Triangle CFD  s similar to Triangle BAE

 

So

 

BA / EB = CF / DC      which means that

 

BA * DC   =  EB * CF    but EB = CF

 

So

 

BA * DC =  EB^2

 

28 * 58  = EB^2   =  area of square BCFE  = 1624 units^2

 

 

cool cool cool

 Nov 5, 2018

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