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 November 11th, 2011, 11:34 AM #1 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,682 Thanks: 699 Similar rectangles Found this one quite interesting... Code: A E B ______________________ | | | | | | | | | | | | | F |________| H | | | | | | |____________|________| D G C Rectangle ABCD is subdivided into 3 rectangles as shown. All 4 rectangles are similar: AB/AD = AD/AE = EF/EB = FH/FG Area of rectangle AEGD = u square units Area of rectangle FHCG = v square units u = v + 20000 square units What's the area of rectangle EBHF?
November 11th, 2011, 01:23 PM   #2
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Re: Similar rectangles

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 Originally Posted by Denis Found this one quite interesting... Code: A E B ______________________ | | | | | | | | | | | | | F |________| H | | | | | | |____________|________| D G C Rectangle ABCD is subdivided into 3 rectangles as shown. All 4 rectangles are similar: AB/AD = AD/AE = EF/EB = FH/FG Area of rectangle AEGD = u square units Area of rectangle FHCG = v square units u = v + 20000 square units What's the area of rectangle EBHF?
Well one way to express the area is DG x FG. But I get the feeling that you are looking for something else.

November 11th, 2011, 01:28 PM   #3
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Re: Similar rectangles

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 Originally Posted by mrtwhs Well one way to express the area is DG x FG. But I get the feeling that you are looking for something else.
Are you serious?
Calculate the ACTUAL area. Answer will contain 4 digits, ok?

November 11th, 2011, 02:53 PM   #4
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Re: Similar rectangles

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Originally Posted by Denis
Quote:
 Originally Posted by mrtwhs Well one way to express the area is DG x FG. But I get the feeling that you are looking for something else.
Are you serious?
Calculate the ACTUAL area. Answer will contain 4 digits, ok?
I was serious. I just forgot to mention that DG x FG = 5000.

November 11th, 2011, 06:09 PM   #5
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Re: Similar rectangles

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 Originally Posted by mrtwhs I was serious. I just forgot to mention that DG x FG = 5000.
No it's not: it equals 10000. Got you with my "4 digits"!?

 November 13th, 2011, 06:11 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,048 Thanks: 1395 Since 10000 has five digits, it is deliberately misleading to understate the number of digits as four. If the area to be found is w square units, u, w and v are the first, second and fourth terms of a geometric progression with common ratio (?5 + 1)/2. It's easy to confirm that w = 10000.
November 13th, 2011, 06:51 PM   #7
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 Originally Posted by skipjack Since 10000 has five digits, it is deliberately misleading to understate the number of digits as four.
Agree; BUT I did this on purpose, as a joke, as I thought Mrtwhs was joking with his 1st reply;
joke meant same way as ye olde "how many months have 28 days? ALL of them!"

November 13th, 2011, 07:00 PM   #8
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 Originally Posted by skipjack If the area to be found is w square units, u, w and v are the first, second and fourth terms of a geometric progression with common ratio (?5 + 1)/2.
If we let FH = 1, then FG = SQRT{[SQRT(5) - 1] / 2}, or ~.78615

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