MathDB

6

Part of 2018 Puerto Rico Team Selection Test

Problems(1)

sequence of equilaterals on sides of equilateral

Source: Puerto Rico Ibero IMO TST 2018.6

9/16/2021
Starting from an equilateral triangle with perimeter P0P_0, we carry out the following iterations: the first iteration consists of dividing each side of the triangle into three segments of equal length, construct an exterior equilateral triangle on each of the middle segments, and then remove these segments (bases of each new equilateral triangle formed). The second iteration consists of apply the same process of the first iteration on each segment of the resulting figure after the first iteration. Successively, follow the other iterations. Let AnA_n be the area of the figure after the nn- th iteration, and let PnP_n the perimeter of the same figure. If An=PnA_n = P_n, find the value of P0P_0 (in its simplest form).
geometryalgebra