Midpoints of an equilateral triangle
One side of an equilateral triangle is 101 inches. The midpoints of its sides are joined to form another triangle whose midpoints, in turn, are joined to form still another triangle. This process continues indefinitely.
Find the sum of the perimeters of all these triangles that are defined above.
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1 solution
S = a / (1 - r)
Since we're taking it at midpoints, r = 1/2.
S = (3 sides × 101 inches per side) / (1 – 1/2)
= 303 / (1/2)
= 606 inches