15 3/16 inches

Complete Solution:
Complete the table begun in "Get Started:"

 Figure Number Side Length of Each White Triangle (inches) Perimeter (p) of each white triangle p = 3 × side length (inches) Total Number (n) of White Triangles Sum (np) of the perimeters 1 1 3 1 3 2 1/2 3/2 3 9/2 3 1/4 3/4 9 27/4 4 1/8 3/8 27 81/8 5 1/16 3/16 81 243/16

As the figure numbers increase, the side length of each white triangle is halved, and the number of white triangles is tripled. This means the sum of the perimeters in any particular figure is:

3 × 1/2 or
3/2 the sum in the previous figure

The sum of the perimeters in Figure 5 would be 243/16 or 15 3/16 inches.

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