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#1 2010-06-30 15:50:19

lakeheadca
Member
Registered: 2010-01-31
Posts: 37

Square problem:

ABCD is a square with area 9. efgc is a square in which EC=1/3(BC). HIJC is s square in which HC=1/3(EC). If this pattern is continued so that there are a total of ten squares with common vertex at C. and in which each square lies inside its predecessor, what is the area of the tenth square?
Answer: 9^-8

View Image: FIG.JPG

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#2 2010-06-30 19:17:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Square problem:

Hi lakeheadca;

That answer is correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2010-07-01 03:30:54

lakeheadca
Member
Registered: 2010-01-31
Posts: 37

Re: Square problem:

how to solve this problem. please explain!

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#4 2010-07-01 03:46:35

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,257

Re: Square problem:

ABCD has area    3    x    3     =    9     =    9 ^   1
EFCG has area     1    x    1     =    1     =    9 ^   0
HICJ has area    1/3   x   1/3   =   1/9   =    9 ^   -1
KLCM has area   1/9   x   1/9   =  1/81  =    9 ^   -2
.....                           ....                   .....               
10th square has area 3^ -8  x   3 ^ -8  =    9 ^   -8


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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