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October 15th, 2013, 07:21 AM  #1 
Newbie Joined: Oct 2013 Posts: 1 Thanks: 0  Geometrical and Investigative Problem !!! :(
Please Answer with steps for Question 15 in given attachement ! Please

October 15th, 2013, 09:11 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,290 Thanks: 1023  Re: Geometrical and Investigative Problem !!! :(
WHERE is #15? 
October 15th, 2013, 04:18 PM  #3  
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Geometrical and Investigative Problem !!! :( Quote:
 
October 16th, 2013, 04:31 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,929 Thanks: 1124 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 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
[attachment=0:2fybxyec]SquareABCD.PNG[/attachment:2fybxyec]

October 16th, 2013, 11:02 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,290 Thanks: 1023  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  
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Geometrical and Investigative Problem !!! :( Quote:
 
October 18th, 2013, 07:14 AM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,290 Thanks: 1023  Re: Geometrical and Investigative Problem !!! :( Quote:
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 !!! :( 
October 22nd, 2013, 08:39 AM  #10  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,290 Thanks: 1023  Re: Geometrical and Investigative Problem !!! :( Quote:
 

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