SOLUTION: The middlepoints of the side of a triangle are joined forming a second triangle.Again a third triangle is formed by joining the middles points of this second triangle and this proc

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Question 201375: The middlepoints of the side of a triangle are joined forming a second triangle.Again a third triangle is formed by joining the middles points of this second triangle and this process is repeated infinitely.If the perimeter and area of the outer triangle are P and A respectively,What will the sum of perimeters of the triangles thus formed?
Answer by solver91311(12126) (Show Source):
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If you join the mid-points of two sides of a triangle then you form a smaller similar triangle the sides of which are each one-half the measure of the sides of the original triangle, hence the perimeter of the smaller triangle is also one-half the perimeter of the original. If the perimeter of the first triangle is , then the perimeter of the smaller triangle is . The next one would be , and so on.

Therefore the sum of the perimeters would be:

But since

The sum of the perimeters becomes:

John