My Math Forum Geometrical and Investigative Problem !!! :(

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October 15th, 2013, 07:21 AM   #1
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Geometrical and Investigative Problem !!! :(

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 October 15th, 2013, 09:11 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: Geometrical and Investigative Problem !!! :( WHERE is #15?
October 15th, 2013, 04:18 PM   #3
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Re: Geometrical and Investigative Problem !!! :(

Quote:
 Originally Posted by Denis WHERE is #15?
You have to scroll down with your cursor on the attachment.

 October 16th, 2013, 04:31 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Geometrical and Investigative Problem !!! :( Let's make the sides of the square 11 units, so that |AE| = 6 and |BE| = 5. Then the area of quadrilateral BCDE is 88 and the area of triangle CDE is 121/2. Since the median of a triangle divides the triangle into two equal areas (midpoint theorem), the area of triangle CDF is 121/4, so the area of quadrilateral BCFE is 88 - 121/4 = 231/4. Continuing with the midpoint theorem, the area of triangle CDG is 121/8, the area of triangle CDH is 121/16 and the area of triangle CDI is 121/32. Hence area of CDI / area of BCFE = (121/32)/(231/4) = 11/168.
October 16th, 2013, 06:25 AM   #5
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[attachment=0:2fybxyec]SquareABCD.PNG[/attachment:2fybxyec]
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 October 16th, 2013, 11:02 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: Geometrical and Investigative Problem !!! :( Thanks Skip; finally I see the damn thing; Eddy's "scrolling" way no did work for li'l ole me! Just an observation: why d'heck did the "teacher" not simply say: point E is on side AB of square ABCD; AE = 6, BE = 5.
October 17th, 2013, 05:30 PM   #7
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Re: Geometrical and Investigative Problem !!! :(

Quote:
 Originally Posted by Denis why d'heck did the "teacher" not simply say...AE = 6, BE = 5.
Maybe it's because AE=12/11 and BE=10/11.

October 18th, 2013, 07:14 AM   #8
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Re: Geometrical and Investigative Problem !!! :(

Quote:
Originally Posted by eddybob123
Quote:
 Originally Posted by Denis why d'heck did the "teacher" not simply say...AE = 6, BE = 5.
Maybe it's because AE=12/11 and BE=10/11.
Of course AE=12/11 and BE=10/11, Eddy; BUT you're missing my point.
Above is because 4 was given as area of square, with AE:BE = 6:5.

My point is WHY would the teacher use 4 when 121 could be used
giving SAME results, i.e. 11/168

The point of the problem is not to have the student play with fractions,
(like why 12/11 and 10/11 when 6 and 5 will do same thing?)
but to find a way to end with 11/168 as solution.

Anyway, using Greg's method (thanks for using 6 and 5 Greg!!):
k = side length (11)
a = AE (6)
General case formula:
CDI / BCFE = k / [8(3k - 2a)] ........ = 11/168

 October 22nd, 2013, 02:19 AM #9 Newbie   Joined: Oct 2013 Posts: 9 Thanks: 0 Re: Geometrical and Investigative Problem !!! :( For no. 13 see YouTube http://youtu.be/8NwVsbqrzKE
October 22nd, 2013, 08:39 AM   #10
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Re: Geometrical and Investigative Problem !!! :(

Quote:
 Originally Posted by nubian123 For no. 13 see YouTube http://youtu.be/8NwVsbqrzKE
The OP did not ask for help on no.13.

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