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November 11th, 2011, 11:34 AM   #1
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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?
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November 11th, 2011, 01:23 PM   #2
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Re: Similar rectangles

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

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

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

Quote:
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"!?
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November 13th, 2011, 06:11 PM   #6
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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.
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November 13th, 2011, 06:51 PM   #7
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Re:

Quote:
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!"
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November 13th, 2011, 07:00 PM   #8
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Re:

Quote:
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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