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Question

# One side of an equilateral triangle is 24cm. The mid-points of its sides are joined to form another triangle whose mid-points are in turn joined to form still another triangle. This process continues indefinitely. Then the sum of the perimeters of all the triangles is?

A
144cm
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B
213cm
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C
288cm
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D
172cm
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Solution

## The correct option is B 144cmWhen a triangle is formed by joining the midpoints of a triangle, its side-lengths will be half of the original triangle. Therefore, its perimeter will also be halved.Perimeter of original triangle: 24x3=72Perimeter of next triangle: 722=36Perimeter of next triangle: 362=18 and so on...Thefore, total perimeter: 72+36+18+...=72(1+12+14+...)=72(11−12)=144Formula used:a+ar+ar2+ar3+...=a1−r for |r|<1

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