Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Find the sum of a finite geometric series.

The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the length of the outer triangle. This process is continued until three triangles are inscribed in the first triangle. The sum of the perimeters of all four triangles is __________
inches.