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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: 86,636

Re: Square problem:

Hi lakeheadca;

That answer is correct.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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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: 6,393

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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