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tejas ramkumar Grade: 11
        One side of an equilateral triangle is 24cm. The mid points of its sides are joined to form another triangle. Again , joining the mid points of this triangle forms  another triangle and the process is continued infinitely. Determine the sum of the perimeters of all such triangles. 
7 years ago

Answers : (1)

Pratham Ashish
17 Points
										

hi,


for first triangle perimeter = 3 *24 = 72


 for second , ( its sides would be half the first one  )


                   perimeter =  3 * 24 /2  = 72 /2


for third , perimeter =  3 * (24/2 )/2  = 72 / 4


and so on 


so the sum of perimeter will be =  


     72 + 72/2 +72 /4 +72/ 8 + .......................


= 72 ( 1 + 1/2 +1/4 + 1/8 +........................)


 = 72 { 1/( 1-1/2) }                  { sum of ∞ g.p. = a/ 1-r )


= 72 *2


 = 144 cm


 


 


 

7 years ago
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