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 $BCFE$?

1624 units²

Step-by-step explanation:

See attachment for the figure

As, ∠EAB  = ∠CFD

and ∠ABE  = ∠FCD

We can say that by AA congruency,  ΔCFD  is similar to ΔBAE

Therefore, BA / EB = CF / DC      

BA x DC   =  EB x CF    (since EB = CF )

BA x DC =  EB²

28 x 58  = EB²   =>  area of square BCFE

area of square BCFE = 1624 units²

Therefore, the area of square BCFE is 1624 units²

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