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Math Forum » Discussions » Math Topics » geometry.puzzles.independent

Topic: Rectangle Area
Replies: 11   Last Post: Jan 14, 2010 1:01 PM

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Avni Pllana

Posts: 513
Registered: 12/6/04
Re: Rectangle Area
Posted: Jan 6, 2010 5:41 AM
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> > 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.


Hi Steve,

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.

Best regards,
Avni



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