Question

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.

Answer 1

Answer with explanation:

⇒Perimeter of Any Triangle=Sum of three Sides of triangle

Perimeter of Equilateral Triangle having side 16 inches =16+16+16=48 inches

Now, 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.

Perimeter of Second Triangle = 8+8+8=24 inches

Perimeter of Third Triangle = 4 +4+4=12 inches

Perimeter of fourth Triangle = 2 +2+2=6 inches

The sum of the perimeters of all four triangles in inches

=48 +24+12+6

=90 inches