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Steve B
Posts:
15
Registered:
12/8/09


Re: Rectangle Area
Posted:
Jan 5, 2010 5:10 PM


> 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.



