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The midpoints of the three sides of an equilateral triangle are connected to form a second triangle. A third triangle is formed by connecting the midpoints of the second triangle. This process is repeated until a tenth triangle is formed. What is the ratio of the perimeter of the tenth triangle to that perimeter of the third triangle? By midpoints of the second triangle I mean the midpoints of it's sides.

 Apr 16, 2021
 #1
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Com'on just bc it's long doesnt mean it's hard

 Apr 16, 2021
 #2
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ok...........

WillBillDillPickle  Apr 16, 2021
 #3
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HELPPPPpp

 Apr 16, 2021
 #4
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The ratio is 1/16.

 Apr 16, 2021
 #5
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wrong

Guest Apr 16, 2021
 #6
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The  perimeter  of each successive  triangle  is   (1/2)  of  the previous triangle

 

Call the  perimeter  of  the  first  triangle  =  P

 

The  perimeter  of  the nth  triangle  is   P (1/2)^(n - 1)

 

So...the perimeter of  of  the 10th triangle  is   P(1/2)*(10-1)  =  P(1/2)^9

 

The perimeter of the 3rd  triangle is  P(1/2)^(3 - 1)  = P(1/2)^2

 

The  ratio  of the perimeter  of the 10th triangle to the perimeter of the  3rd  triangle  is

 

(1/2)^9  / ( 1/2)^2   =    (1/2)^7  =   1 / 128    

 

 

cool cool cool

 Apr 16, 2021
 #7
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Correct laugh

Guest Apr 17, 2021

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