Math Is Fun Forum

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square problem:

Hi lakeheadca;

That answer is correct.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

lakeheadca

Member

Registered: 2010-01-31

Posts: 37

Re: Square problem:

how to solve this problem. please explain!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

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

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