SOLUTION: An equilateral triangle has a perimeter of 12 cm. By joining the midpoints of its sides with the segments, a second equilateral triangle is formed. This procedure is continued infi

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Question 1086781: An equilateral triangle has a perimeter of 12 cm. By joining the midpoints of its sides with the segments, a second equilateral triangle is formed. This procedure is continued infinitely for each new triangle that is formed. Determine the sum of the perimeters of all triangles, including the original triangle formed. Determine the sum of the perimeters of all triangles Solve each problem
Answer by ikleyn(52788) About Me  (Show Source):
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Perimeters make the geometric progression with the first term 12 cm and the common ratio of 1%2F2.


Therefore, the sum is equal to 12%2F%281-%281%2F2%29%29 = 24 cm.