> > Let ABCD be an arbitrary rectangle. Let DEFG be a > > rectangle such that E is an arbitrary point on the > > line through AB, and FG passes through C. If S1 is > > the area of ABCD, determine the area S2 of DEFG. > > > > Best regards, > > Avni > > Because the puzzle asks us to determine the area, > rather than IF we can determine the area with the > information given, I can conclude that the > information given is sufficient to determine the > area. Therefore I need only determine the area of one > rectangle meeting the description above. > > In particular, I can choose ABCD so that AB > 2*AD. > Take as E one of the two points at which the circle > of which CD is the diameter intersects AB. So angle > DEC is a right angle and the rectangle DECG meets the > specified conditions. The area of triangle DEC is 1/2 > of the area of ABCD and 1/2 the area of DECG, so S2 = > S1.
your solution is correct, and many thanks for the nice conrtibution. The problem can also be solved using trigonometry and dissection, and I hope someone will post solutions using those techniques.