Question

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

Answer 1

90 inches

Explanation:

The perimeter of the inscribed triangle is 1/2 that of the enclosing triangle. So, the total of perimeters is ...

(3·16 in)(1 +1/2 +1/4 +1/8) = (48 in)(15/8) = 90 inches