WMC 2018 Senior Problem 20

Level 1

Start with an equilateral triangle of side $2$ . Form a second equilateral triangle by connecting the midpoints of the first triangle. Form a third equilateral triangle by connecting the midpoints of the second triangle. If you continue this process indefinitely, what is the sum of the areas of all the triangles?

\frac { 1 }{ 3 }

\frac{4\sqrt3}{3}

\frac{5\sqrt3}{3}

\frac{7\sqrt3}{3}

\frac{8\sqrt3}{3}

1 solution

X X
Oct 14, 2018

The area of an equilateral triangle of side 2 is equal to $\sqrt{3}$

$\sqrt{3}(1+\frac14+\frac1{16}+\frac1{64}+...)=\sqrt{3}\times\frac43$

WMC 2018 Senior Problem 20

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