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An equilateral triangle T2 is formed by joining the mid points of the

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An equilateral triangle T2 is formed by joining the mid points of the [#permalink]

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An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 40 cm, find the sum of the perimeters of all the triangles.

A. 180 cm
B. 220 cm
C. 240 cm
D. 270 cm
E. 300 cm


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[Reveal] Spoiler: OA

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Re: An equilateral triangle T2 is formed by joining the mid points of the [#permalink]

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hdwnkr wrote:
An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 40 cm, find the sum of the perimeters of all the triangles.

A. 180 cm
B. 220 cm
C. 240 cm
D. 270 cm
E. 300 cm


In dire need of kudos.


We have 40 for first triangle, when we join mid-points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues.

So we have 40,20,10,...

We have ratio = 1/2, and it is GP type.

Sum of infinite triangle is a/1-r = 40/1-(1/2) = 80

Equilateral triangle perimeter is 3a = 3*80 = 240.

So option C.

Let me know if I am missing anything.

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Re: An equilateral triangle T2 is formed by joining the mid points of the [#permalink]

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New post 07 Oct 2017, 02:17
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Re: An equilateral triangle T2 is formed by joining the mid points of the   [#permalink] 07 Oct 2017, 02:17
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