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 $BCFE$?
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
BA * DC = EB^2
28 * 58 = EB^2 = area of square BCFE = 1624 units^2
