SOLUTION: Mid-points of the side of an equilateral triangle of side 18 cm are joined to form another triangle, whose mid-points are further joined to form a different triangle and this p

Question 876826: Mid-points of the side of an equilateral
triangle of side 18 cm are joined to form
another triangle, whose mid-points are
further joined to form a different triangle and
this process is repeated indefinitely. The sum
of the perimeters of all the triangles will be
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
The perimeter of the original triangle is 3*18=54cm. The triangle formed by the first midpoint connection has sides of 9cm. Its perimeter is 3*9cm = 27cm. The third triangle has sides of 4.5cm. Its perimeter is 3*4.5cm = 13.5cm.

The total perimeter is 3*(18+9+4.5+...)

18+9+4.5... is a geometric series 18/(2^n) where n is 0 to infinity.

The sum of an infinite geometric series xr^0+xr^1+xr^2+...xr^n+... converges to a certain value which is x/(1-r). In this case x=18 and r=1/2. So the sum is 18/(1/2) = 18*2 =36.

The total perimeter is 3*36 = 108 cm.

RELATED QUESTIONS
three side of equal length, x, cm, are joined to form an equilateral triangle. if the... (answered by Fombitz)

Find the area of an equilateral triangle inscribed in a circle circumscribed by a square... (answered by addingup,greenestamps)

In the triangle below, one vertex is joined to two points on the opposite side of the... (answered by greenestamps,ikleyn)

I have an equilateral triangle with Base: 35 Mid segment: 20 Side below mid: 12 I... (answered by KMST)

there is a fingur given and the question is In a triangle ABC,D,E,F are respectively the (answered by solver91311)

ABCD is parallelogram and M,N ARE MID POINTS OF THE SIDES BC,AD RESPECTIVELY . PROVE THAT (answered by ichigo449)

A side of an equilateral triangle is 10 cm. the midpoints of its sides are joined to form (answered by reviewermath)

Find the are of an equilateral triangle of side... (answered by Theo)

Hi - another question we have is "A line passing through the mid-point of one side of a... (answered by stanbon)