Date: Jan 5, 2010 5:10 PM
Author: Steve B
Subject: Re: Rectangle Area

> 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.